Question

A jogger runs 6 miles per hour faster downhill than uphill. If the jogger can run 5 miles downhill in the same time that it takes to run 2 miles uphill find the jogging rate in
each direction

Answer 1

Answer:

The speed of jogger in uphills is 4 mile per hour  

And  The speed of jogger in downhills is 10 mile per hour

Step-by-step explanation:

Given as :

The distance cover by jogger in downhill (Dd) = 5 miles

The distance cover by jogger in uphill     (Du)  = 2 miles

The time taken by jogger in downhill       (Td)  = T  hour

The time taken by jogger in uphill            (Tu)  = T hour

Let The speed of jogger in uphills            (Su)  = x mph

So ,The speed of jogger in downhills      (Sd)  =( x + 6 ) mph

∵, Time = $\frac{Distance}{Speed}$

So, Tu = $\frac{Du}{Su}$

Or, T = $\frac{2}{x}$   h

And Td = $\frac{Dd}{Sd}$

Or,   T = $\frac{5}{(x + 6)}$  h

∵  Time duration of both is same

∴  $\frac{2}{x}$ = $\frac{5}{(x + 6)}$

Or,  2 × (x + 6) = 5x

Or,  2x + 12 = 5x

So,    12 = 3x

∴       x = $\frac{12}{3}$ = 4 mph

And  x + 6 = 4 + 6 = 10 mph

Hence The speed of jogger in uphills is 4 mile per hour  

And      The speed of jogger in downhills is 10 mile per hour   Answer