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.
