Question

1. Suzette ran and biked for a total of 110 mi in 7 h. Her average running speed was 5 mph and her average biking speed was 20 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?

Answer 1

Answer:

Part a) Suzette ran 2 hours

Part b) Suzette biked 5 hours

Step-by-step explanation:

Let

x ------> total hours Suzette ran

y -----> total hours Suzette biked

we  know that

x+y=7

x=7-y -----> equation A

5x+20y=110 -----> equation B

Solve the system by substitution

substitute equation A in equation B and solve for y

5(7-y)+20y=110

35-5y+20y=110

15y=110-35

15y=75

y=5 hours

Find the value of x

x=7-5=2 hours

therefore

Suzette ran 2 hours and biked 5 hours

Check your solution

Her average running speed was 5 mph

so

Find the distance

Multiply the speed by the number of hours

5(2)=10 miles

Her average biking speed was 20 mph

so

Find the distance

Multiply the speed by the number of hours

20(5)=100 miles

Adds the two distances

10 +100=110 miles ------> is correct