a train travel 180 km

A train travels 180 km at a uniform speed. If the speed had been 9km/hour more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Given: Distance travelled by the train = 180 km.

Let the speed of train = x km/hr

= (180/x ) hr

Let the increased speed of the train = (x + 9) km/hr

= (180/x + 9) hr

Now, given that the if the speed be (x + 9) km/hr, then the train will take 1 hour less to travel the same distance.

So, according to the question,

Now, solving it further as follows:

⇒ 180x - 180(x + 9) = x (x + 9)

⇒ 180x - 180x - 1620 = x 2 + 9x

⇒ x 2 + 9x - 1620 = 0

⇒ x 2 - 36x + 45x - 1620 = 0

⇒ x (x - 36) + 45(x – 36) = 0

⇒ (x - 36)(x + 45) = 0

⇒ x = 36 or -45

But, speed can’t be negative, therefore speed = 36 km/hr.

Average Speed Calculator

Use this speed calculator to easily calculate the average speed of a vehicle: car, bus, train, bike, motorcycle, plane etc. with a given distance and travel time. Returns miles per hour, km per hour, meters per second, etc.

Related calculators

• Average Speed formula
• How to calculate the average speed of a car?
• Finding average speed examples
• Average speed vs Average velocity

    Average Speed formula

The average speed calculation is simple: given the distance travelled and the time it took to cover that distance, you can calculate your speed using this formula:

Speed = Distance / Time

The metric unit of the result will depend on the units you put in. For example, if you measured distance in meters and time in seconds, your output from the average speed calculator would be ft/s. If distance was measured in miles and time in hours, then output will be in miles per hour (mph, mi/h), and so on for km/h, m/s, etc. - all supported by our tool.

    How to calculate the average speed of a car?

Let us say that you travelled a certain distance with your car and want to calculate its average speed. The easiest way to do that would be by using the speed calculator above, but if you prefer, you can also do the math yourself. Either way, one needs to know the distance. If you have noted the distance on your odometer then you can use that number. Other options are to use a map (e.g. Google Maps) and measure the distance travelled based on your actual path (not via a straight line, unless you travelled by air in which case that would be a good approximation), or to use a GPS reading if you used navigation during the whole trip. Then you need to know the travel time. Make sure to subtract any rests or stops made from the total trip duration.

As you can see, to work out your speed in km/h or mph just apply the speed formula with the relevant units for distance and time. This is how to calculate average speed of a car, bike, boat, or any other vehicle or object.

    Finding average speed examples

Example 1: Using the equation above, find the speed of a train which travelled 120 miles in 2 hours and 10 minutes while making four stops, each lasting approximately 2.5 minutes. First, subtract the time spent at the train stops: 2.5 x 4 = 10 minutes. 2:10 minus 10 minutes leaves 2 hours of travel time. Then, apply the avg speed formula to get 120 miles / 2 hours = 60 mph (miles per hour).

Example 2: A cyclist travels to and from work, covering 10 km each way. It took him 25 minutes on the way to work and 35 minutes on the way back. What is the cyclist's average speed? First, add up the time to get 1 hour total. Also add up the distance: 5 + 5 = 10 kilometers. Finally, replace in the formula to get 10 / 1 = 10 km/h (kilometers per hour) on average in total.

    Average speed vs Average velocity

Average speed (what this calculator computes) and average velocity are not necessarily the same thing though they may coincide in certain scenarios. This is basic physics, but a lot of people find it confusing. Here are the differences in short.

Speed is a scalar value whereas velocity is the magnitude of a vector. Speed does not indicate direction whereas velocity does. The two coincide only when the journey from the start point to the end point happens on a straight line, such as in a drag race. If the movement path is not a straight line then the average velocity will be smaller than the mean speed.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Average Speed Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/average-speed-calculator.php URL [Accessed Date: 22 Jun, 2024].

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Ex 4.1, 2 (iv) - Chapter 4 Class 10 Quadratic Equations

Last updated at April 16, 2024 by Teachoo

Ex 4.1, 2 Represent the following situations in the form of quadratic equations : (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train. Let Speed of train be x km/hr Normal speed Distance = 480 km Speed = x km/hr Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 x = 480/𝑇𝑖𝑚𝑒 Time = 𝟒𝟖𝟎/𝒙 Speed became 8 km/h less Distance = 480 km Speed = (x – 8) km/hr Time = 480/𝑥 + 3 Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒 x – 8 = 480/((480/𝑥 " + 3" ) ) (x – 8) (𝟒𝟖𝟎/𝒙 " + 3" ) = 480 From (1) (x – 8) (𝟒𝟖𝟎/𝒙 " + 3" ) = 480 (x – 8) ( (480 + 3𝑥)/𝑥) = 480 (x – 8) (480 + 3x) = 480 x x (480 + 3x) – 8 (480 + 3x) = 480 x 480x + 3x2 – 3840 – 24x = 480 x 480x + 3x2 – 384 – 24x – 480 x = 0 3x2 + 480x – 480x – 24x 3840 = 0 3x2 – 24x – 3840 = 0 3 (x2 – 8x – 1280) = 0 x2 – 8x – 1280 = 0/3 x2 – 8x – 1280 = 0 It is the form of ax2 + bx + c = 0 Where a = 1, b = – 8 , c = –1280 Hence, it is a quadratic equation .

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A train travels at a speed of 180 km/h. How far will it travel in 4 hours?

Speed of train v = 180 k m / h time taken t = 4 h so, distance cover by train d = v t ⟹ d = 180 × 4 = 720 k m.

A train A travelled a distance of 120km in 3 hours whereas another train B travelled a distance of 180km in 4 hours. Which train travelled faster?

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Railways conducts trial run on world's highest arch rail bridge in Jammu's Chenab

Indian Railways on Thursday successfully conducted a trial run of an eight-coach MEMU train on the world's highest railway bridge - Chenab Bridge - in Jammu and Kashmir, paving the way for the start of rail service on the route from Reasi to Baramulla in Kashmir. "After an extensive inspection of the newly constructed Chenab Bridge by senior officers from Railway Board, Northern Railway and Konkan Railway, a trial run was conducted on a 46-km-long electrified line section between Sangaldan in Ramban district and Reasi at a speed of 40 kmph," the Railway Ministry said in a statement. "It was successfully carried out starting at 12:35 pm from Sangaldan and reaching Reasi at 2:05 pm. On the way it passes through nine tunnels with a combined length of 40.787 km and the longest tunnel T-44 of 11.13 km," it added.

Three stations According to the ministry, it was the first ever full train that crossed over the iconic bridge between Dugga and Bakkal stations across the Chenab River, the world's highest arch railway bridge. The stations - Reasi, Bakkal, Dugga and Sawlakote - are situated in the Reasi district of J&K. "The electrification work on this section has been executed with state-of-the-art technology, ROCS (Rigid Overhead Conductor System) at 25 kV, for the first time on railways," the ministry said. Upon the mainline electric multiple unit (MEMU) train's arrival at Reasi railway station, chants of 'Bharat Mata ki Jai' echoed as a large crowd gathered to witness the historic event. The train carried employees working on the project as well as railway officials.

In February 2024, the first electric train trial run from Banihal to Khari to Sangaldan section on the Banihal-Katra section of the USBRL project in Ramban was successfully conducted on around 40 km of track and tunnels between Banihal and Sangaldan railway stations in Ramban district. "After conducting a series of such tests, this bridge would be open to run all train services which will be a monumental stride towards the seamless integration of the Kashmir valley with Jammu and the broader Indian landscape," the ministry said. It added, "This would foster social integration by facilitating easier movement of people and goods, thereby promoting cultural exchanges and regional development and boost to economic activities such as tourism and trade." 

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A bus travels 180 k m in 3 hours and a train travels 450 k m in 5 hours. Find the ratio of speed of train to speed of bus.

Find speed of bus and train given, distance travelled by the bus = 180 k m time taken by the bus to cover the given distance = 3 hours distance travelled by the bus = 450 k m time taken by the bus to cover the given distance = 5 hours we know that, speed = distance travelled time taken thus, speed of bus = 180 k m 3 h o u r s = 60 k m / h r and, speed of train = 450 k m 5 h r s = 90 k m / h r ratio of speed of train to speed of bus = speed of train speed of bus = 90 60 = 9 6 now, further simplifying the above ratio or fraction into its lowest form by dividing the numerator and denominator by 3 , we get 9 6 = 9 ÷ 3 6 ÷ 3 = 3 2 = 3 : 2 therefore, the ratio of the speed of the train to the speed of the bus is 3 : 2 ..

A bus travels 126 km in 3 hours and a train travels 315 km in 5 hours at uniform speeds. Find the ratio of distances covered by them in one hour.

A bus travels 126 k m in 3 hours and a train travels 315 k m in 5 hours . Find the ratio of their speeds .

A train travels 240 k m i n 3 h o u r s and a bus travels 140 k m i n 2 h o u r s . Find the ratio of their speeds.