Question

17. (a) If a car increases its speed by 10 km/h then it takes 36 minutes less to cover a distance of
72 km. Find the original speed of the car.
(b) An express train makes a run of 240 km at a certain speed. Another train whose speed is 12
km/h less takes an hour longer to make the same trip. Find the speed of the express train.
(c) A mail train takes 2 hours less than a passenger train to cover 192 km. If the speed of the mail
train is 16 km/h more than that of the passenger train, find the speed of the passenger train.
(d) The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car
travels at a speed of x km/h and a train travels faster by 16 km/h. Calculate
(i) the time taken by the car to reach town B from A, in terms of x, and
(ii) the time taken by the train to reach town B from A, in terms of x.
If the train takes 2 hours less than the car, obtain an equation in x. Solve it and find the speed of
the train.

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Answer 1

Step-by-step explanation:

(a)Let the original speed of the car =xkm/hr

∴ Time taken by it to cover 72km=

x

72

hrs

New speed of the car = (x+10)km/hr

∴ New time taken by the car to cover 72km=

x+10

72

hrs

As per the given condition, time is reduced by 36 minutes

∴

x

72

−

x+10

72

=

60

36

x

2

+10x−1200=0

(x−30)(x+40)=0

On solving we get, x=−40 or x=30

Since the speed cannot be negative, so x=30km/hr.