Question

As part of her training routine for basketball, Shaylle alternates between cycling and running for exercise. She cycles at a rate of 10mph and runs at a rate of 6 mph. If she spends 4.5 hours exercising and covers a total of 41 miles, how much time did she spend on each exercise

Answer 1

The time taken while cycling is 1 hour

The time taken on running is 3.5 hours

Explanation:

Given as :

The speed at which Shaylle cycles = 10 miles per hour

The speed at which Shaylle runs = 6 miles per hour

The Total Time she spend on both exercise = 4.5 hours

Let The time taken on cycle =
`t_1` hours = t hour

And The time taken on exercise =
`t_2` = (4.5 -t) hours

The Total Distance she cover = 41 miles

Let The distance cover by her on cycles =
`d_1`

And The distance cover by her on exercise =
`d_2`

Now, According to question

Distance = Speed × Time

So, For Cycling

`d_1` = 10 mph ×
`t_1`

Or,
`d_1` = 10 mph × t hours

Or ,
`d_1` = 10 t miles

For exercise

`d_2` = 6 mph ×
`t_2`

Or,
`d_2` = 6 mph × (4.5 - t) hours

Or ,
`d_2` = (27 - 6 t) miles

Now, Distance =
`d_1` +
`d_2`

Or , D =
`d_1` +
`d_2`

or, 10 t miles + ( 27 - 6 t) miles = 41 miles

Or, 10 t - 6 t = 41 - 27

Or, 4 t = 14

∴ t =
`(14)/(4)`

I.e t = 3.5 hours

So, The time taken on cycle =
`t_1` hours = t hour

I.e
`t_1` = 3.5 hours

And The time taken on exercise =
`t_2` = (4.5 - t) hours

I.e
`t_2` = 4.5 - 3.5 = 1 hour

Hence The time taken while cycling is 1 hour

And The time taken on running is 3.5 hours Answer