The Average speed of a train in is 20 MPH faster than that of a car. In 8hr. and 40min. the train covers the?

Question

The Average speed of a train in is 20 MPH faster than that of a car. In 8hr. and 40min. the train covers the same distance that the car covers in 13 hours. Find the Average speed of each

Answer 1

Let T be the avg. speed of the train and C the avg. speed of the car.

Avg. speed of train is 20 MPH more so
1.) T = C + 20

Let DT & DC be the distance traveled by the train and car respectively.

The distances are the same so

2.) DT = DC

Since distance = rate * time, if we let TT & TC be the times for the train and car respectively, we have

3.) T * TT = C * TC

If we substitute formula 1 in we get

4.) (C + 20) * TT = C * TC
C * TT + 20 * TT = C * TC
20 * TT = C * TC - C * TT
20 * TT = C (TC - TT)
C = (20 * TT) / (TC - TT)

If we substitute the times we have given, we have

C = (20 * 8.66...) / (13 - 8.66...) = 40

Since T = C + 20, T = 60

So the train's avg. speed is 60 MPH and the car's is 40 MPH

Answer 2

first you should set up your equations. Average speed = distance/time. SInce you know the train is faster than the car by 20MPH, you can use that info to substitute the train's speed by denoting (C + 20) as the train's average speed. This gives you an equation traveled by the train, which is C+20=Distance/(26/3 hr). Then you know it took the car 13 hours to finish a certain distance. This gives another equation..Car's avg speed = distance/13hrs. Combining both equations to get rid of the distance. At the end, just find C for car's avg speed, then you'll know the train's. The answer is: 40 MPH for car, and 60 MPH for train.

Answer 3

The distance is constant, so you can make 2 equations solving for distance:

26/3 hours * (v + 20 MPH) = distance
13 hours * v = distance

Set the equations equal to eachother since distance is the same in both equations and solve for v (average speed of the car) then add 20 MPH for the average speed of the train.

Answers below when you solve.
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Train = 60, Car = 40
Now check your answer by plugging back into your original equations to check that the distance comes out to be the same for both.

Answer 4

let the speeds of the car and the train be 'x' and 'x+20' mph respectively.the equation is
82/3*(x+20)=13x => 26/3x+520/3=13x =>26x+520=39x=>
13x=520 and therefore the speed of the car is 40 mph and that of the train is 40+20=60 mph

Answer 5

Set up an equation.

Remember all these type problems are based on the formula:

distance = rate x time

(e.g. 100 miles = 50 MPH x 2 hours)

Good luck.