Question

a man travels 70km at a certain average speed on a dual carriage way. He then reduces his speed by 30km per hour to cover a distance of 50km on a bad road. If the time taken is the same for both parts of the journey, calculate
(A) his speed for each part of the journey.
(B) the average speed for the whole journey. ​

Answer 1

Answer:

A. (105 kmph, 75 kmph) ;

B. 90 kmph

Step-by-step explanation:

Time taken for each part = t hrs

Speed in first 70 km = x kmph

Speed in next 50 km = (x - 30) kmph

In first part of the journey

x = 70/t .....(1)

In second part of the journey

x - 30 = 50/t ......(2)

Divide equations (1) and (2)

x/(x - 30) = (70/t) / (50/t)

x/(x - 30) = 7/5

5x = 7x - 210

2x = 210

x = 210/2

x = 105 kmph

Speed in second part of the journey is then 105 kmph - 30 kmph = 75 kmph

From equation (1)

x = 70/t

t = 70/x

t = 70/105

t = 2/3 hr

Total journey time = 2/3 hr + 2/3 hr = 4/3 hr

Average speed of whole journey

V = Total Distance / Total Time

= (70 km + 50 km) / (4/3 hr)

= (120 × 3/4) kmph

= 90 kmph