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

Answer:

The time taken while cycling is 1 hour

The time taken on running is 3.5 hours

Step-by-step 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 = $\frac{14}{4}$

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