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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

Respuesta :

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 = [tex]t_1[/tex] hours = t hour

And The time taken on exercise = [tex]t_2[/tex] = (4.5 -t) hours

The Total Distance she cover = 41 miles

Let The distance cover by her on cycles = [tex]d_1[/tex]

And The distance cover by her on exercise = [tex]d_2[/tex]

Now, According to question

Distance = Speed × Time

So, For Cycling

[tex]d_1[/tex] = 10 mph × [tex]t_1[/tex]

Or, [tex]d_1[/tex] = 10 mph × t hours

Or ,  [tex]d_1[/tex] = 10 t  miles

For exercise

[tex]d_2[/tex] = 6 mph × [tex]t_2[/tex]

Or, [tex]d_2[/tex] = 6 mph × (4.5 - t)  hours

Or ,  [tex]d_2[/tex] = (27 - 6 t)  miles

Now, Distance = [tex]d_1[/tex] + [tex]d_2[/tex]

Or ,  D =  [tex]d_1[/tex] + [tex]d_2[/tex]

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

Or,  10 t - 6 t =  41 - 27

Or, 4 t = 14

∴  t = [tex]\frac{14}{4}[/tex]

I.e t = 3.5 hours

So, The time taken on cycle = [tex]t_1[/tex] hours = t hour

I.e  [tex]t_1[/tex] = 3.5 hours

And The time taken on exercise = [tex]t_2[/tex] = (4.5 - t) hours

I.e  [tex]t_2[/tex] = 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