The time taken by a person to travel an upward distance of 150 km was $2\frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of 10 km/h more than the s

Question

The time taken by a person to travel an upward distance of 150 km was $2\frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of 10 km/h more than the speed while going up, find the speeds in each direction.

Accepted Answer

Step 1: Let the speed in upward direction be $x$ km/h and the speed in downward direction $= (x + 10)$ km/h.
ATQ:
Step 2: $\frac{150}{x} - \frac{150}{x + 10} = \frac{5}{2}$
$\Rightarrow x^2 + 10x - 600 = 0$
Step 3: $\Rightarrow (x + 30)(x - 20) = 0$
Step 4: $	herefore x = 20$ (rejecting $x = -30$)
and $x + 10 = 20 + 10 = 30$
Step 5: Therefore, speeds in upward and downward direction are 20 km/h and 30 km/h respectively.

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