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

The speed of jogger in uphills is 4 mile per hour

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

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 =
`(Distance)/(Speed)`

So, Tu =
`(Du)/(Su)`

Or, T =
`(2)/(x)` h

And Td =
`(Dd)/(Sd)`

Or, T =
`(5)/((x + 6))` h

∵ Time duration of both is same

∴
`(2)/(x)` =
`(5)/((x + 6))`

Or, 2 × (x + 6) = 5x

Or, 2x + 12 = 5x

So, 12 = 3x

∴ x =
`(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