Suzette ran and biked for a total of 34 mi in 3.5 h. Her average running speed was 6 mph and her average biking speed was 12.5 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution. (a) How many hours did Suzette run? (b) How many hours did she bike?

The speed of an object is the rate of distance traveled over time. Suzette ran for 1.5 hours, and she biked for 2 hours.

Given that:

Speed is calculated as:

Make Distance the subject

Average running speed = 6 mph for x hours implies that:

Average biking speed = 12.5 mph for y hours implies that:

So, the total distance is:

The total distance is 34 miles. So, we have:

The total time is 3.5h. So, we have:

Make x the subject

Substitute in

Collect like terms

Divide both sides by 6.5

Recall that:

Hence, Suzette ran for 1.5 hours, and she biked for 2 hours.

Read more about speed at:

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From the information given

x is time for which she ran at speed of 6mi/h and

y is time for which she biked at speed of 12.5 mi/h

total time = 3.5 h

total distance = 34 mi

so

6x + 12.5y = 34 and

x + y = 3.5

x = 3.5 - y

6 ( 3.5 - y) + y = 34

6.5y = 13 which gives

y = 2 and this

x = 1.5

so suze ran for 1.5 h and biked for 2 h

CHECK

speed of run X time of run + speed of biking x time of biking must be = total distance covered

6 × 1.5 + 12.5 × 2 = 9 + 25= 34 mi

which is true

a

step-by-step explanation: