Suzette ran for 1.5 hours and biked for 4.5 hours
Step-by-step explanation:
The given is:
- Suzette ran and biked for a total of 60 miles in 6 hours
- Her average running speed was 4 mph
- Her average biking speed was 12 mph
- Let x = total hours Suzette ran
- Let y = total hours Suzette biked
∵ x represents the total hours Suzette ran
∵ y represents the total hours Suzette biked
∵ Suzette ran and biked for a total 6 hours
∴ x + y = 6 ⇒ (1)
∵ Her average running speed was 4 mph
∵ Her average biking speed was 12 mph
∵ Distance = speed × time
∴ Her total distance = 4 x + 12 y
∵ Suzette ran and biked for a total of 60 miles
- Equate the two expressions of her total distance
∴ 4 x + 12 y = 60 ⇒ (2)
Now let us solve the system of equations to find the values of x and y
Multiply equation (1) by -4 to eliminate x
∵ (-4) x + (-4) y = (-4)(6)
∴ -4 x - 4 y = -24 ⇒ (3)
- Add equations (2) and (3)
∴ 8 y = 36
- Divide both sides by 8
∴ y = 4.5
∴ Suzette biked for 4.5 hours
- Substitute the value of y in equation (1) to find the value of x
∵ x + 4.5 = 6
- Subtract 4.5 from both sides
∴ x = 1.5
∴ Suzette ran for 1.5 hours
Suzette ran for 1.5 hours and biked for 4.5 hours
Learn more:
You can learn more about system of equations in brainly.com/question/6075514
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