Question

Question : A starts from home for his office. He travels downhill, then on flatground and then uphill to reach his
office. It takes him 3 hrs to reach the office. On the way back home A takes 3 hrs 10 min to reach home along the same
route. The Speeds downhill is 60 km/hr, on flat ground is 48 km/hr and uphill is 40 km/hr.
By what Distance should his office be shifted so that the Time taken to go to the office is same as Time taken to reach
he office?

PLEASE tell correct answer.​

Answer 1

visran AVN parishram parishram ko samjhaie

Answer 2

Distance by which office should be shifted = 20 km

Let d1 be distance from house to flatground, d2 be distance of flatground and d3 be distance of office from flatground.

Let t1,a; t2,a; t3,a be the time taken to go downhill, flat and uphill respectively from the house to office and t1,b; t2,b; t3,b be the same times from office to house respectively.

Thus, it is given that,

t1,a + t2,a + t3,a = 3hrs

t1,b + t2,b + t3,c = 3hrs 10min

Substracting, as time taken to travel flatpart remains same:

t1,b - t1,a + t3,b - t3,a = 10 min = $\frac{1}{6}$ hours

time = $\frac{distance}{speed}$

$\frac{d1}{Su}$ - $\frac{d1}{Sd}$ + $\frac{d3}{Su}$ - $\frac{d3}{Sd}$ = $\frac{1}{6}$

∴ $\frac{1}{40}$(d1 - d3) + $\frac{1}{60}$ (d1 - d3) =  $\frac{1}{6}$

Solving, we get

d3 -d1 = 20 km

As the difference in the routes taken to travel uphill and downhill is 20 km, there is a difference in travelling times to and from the office.

Hence, if the office is shifted downhill 20km the time required to travel both ways will be the same.