Question

Jill was training for a triathlon, so she planned a day of exercising. She spent a total of 2 hours riding her bike and running. She biked for 12 miles and ran for 6 miles. Her rate for running was 10 mph less than her biking rate. What was her rate when running?

Answer 1

Answer:

Jill ran at 5 mph and biked at 15 mph.

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Time Jill spent riding her bike and running = 2 hours = 120 minutes

Distance Jill biked = 12 miles

Distance Jill ran = 6 miles

Speed of running = Speed of biking - 10 mph

2,. What was her rate when running?

For solving this question, we should understand that rate and speed are synonyms.

Speed when Jill was running = x

Speed when Jill was biking = x + 10

Let's recalll that the formula of speed, this way:

Speed = Distance/Time ⇒ Time = Distance/Speed, thus:

6/x + 12/(x + 10) = 2

6(x + 10) + 12x = 2(x + 10) (x); Multiplying by x (x + 10)  at both sides

6x + 60 + 12x = 2x² + 20x

18x + 60 = 2x² + 20x

2x² + 2x - 60 = 0

x² + x - 30 = 0 (Dividing by 2)

(x + 6) (x - 5) = 0 Two solutions for x

x₁ + 6 = 0 ⇒ x₁ = -6

x₂ - 5 = 0 ⇒ x₂ = 5

We take x₂ as the answer because speed or rate can't be negative.

x₂ + 10 = 15

Jill ran at 5 mph and biked at 15 mph.