Question

Sandeep is going from Dehradun to mussoorie and the road is both uphill and downhill and his average speed is 36km/hr on uphill and 72 km/hr on downhill. find the distance between Dehradun to mussoorie if he takes 7hr to make a round trip?
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Answer 1

Answer: 168 km is the distance between Dehradun and Mussoorie.

Given: We are given that uphill speed and downhill speed of Sandeep is 36 km/hr and 72 km/hr respectively. He takes 7 hr to make a round trip.

To Find: We have to find the distance between Dehradun and Mussoorie.

Step-by-Step Explanation: We will take the downhill speed to be u and the uphill speed to be v.

According to question:

u = 72 km/hr

v = 36 km/hr

We know that distance is same in both case that is uphill and downhill.

Let the distance be d

Step 1: During downhill, let the time taken be $t_1$

$72\times t_1=d$

Step 2: During uphill, let the time taken be $t_2$

$36\times t_2=d$

Step 3: Since, both are equal to d, we can equate them.

$72\times t_1=36\times t_2$

$\frac{t_1}{t_2}=\frac{1}{2}$

Now, let $t_1$ be x and $t_2$ be 2x

Step 4: Now, we are given that the total time is 7 hours

$x+2x=7$

$3x=7$

$x=\frac{7}{3}$

This is the value of $t_1$

Step 5: To get the distance between Dehradun and Mussoorie, we will use the equation formed in Step 1:

$72\times \frac{7}{3}$ = 168 km

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