Question

A van travelled at an average speed of 65km/hr from town A. A 35 minutes later a car started from town A ans drove along the same route as the van.If the car caught up with the van after travelling a distance of 130km find the avg speed of the car

Answer 1

91.6 km/h

Explanation:

Let v = average speed of van = 65 km/h and v' = average speed of car. Let t be the time the car starts to move. The van started 35 minutes earlier at t' = (t + 35/60) h.

Since distance d = vt where v = velocity and t = time, the distance moved by the van d = vt' = v(t + 35/60) and that moved by the car is d' = v't.

Since the car catches up with the van after it had moved a distance of 130 km, d = d' = 130 km.

So d = v(t + 0.583)

Substituting d = 130 km and v = 65 km/h, we have

130 km = 65 km/h(t + 0.583)

130 km = (65t + 37.895 )km

subtracting 37.895 from both sides, we have

130 km - 37.895 km = 65t

92.105 = 65t

dividing both sides by 65, we have

t = 92.105/65

= 1.417 h

≅ 1.42 h

Since d = d' = v't,

v' = d'/t

= 130 km/1.42 h

= 91.55 km/h

≅ 91.6 km/h

So, the average speed of the car is 91.6 km/h