Winston and Alice are taking a trip. Winston left at 8am and traveled an average of 50 miles per hour. Alice left at 10am and traveled an average of 70 miles per hour. At what time are they at the same place at the same time? Write a system of equations to represent this situation. Then use the substitution method with that system to determine at what time they will be in the same location. How many miles away from home will they be at that time?

Question

Mathematics

Richard

29 October, 19:24

Winston and Alice are taking a trip. Winston left at 8am and traveled an average of 50 miles per hour. Alice left at 10am and traveled an average of 70 miles per hour. At what time are they at the same place at the same time? Write a system of equations to represent this situation. Then use the substitution method with that system to determine at what time they will be in the same location. How many miles away from home will they be at that time?

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Answers (1)

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Jennifer Huerta · Answer 1

7 hours and 350 miles

Step-by-step explanation:

Winston travels 50 mph for t many hours. This is 50t.

Alice leaves 2 hours later. So if she traveled the same t hours shed have 2 less or t-2. She travels at 70 miles per hour. This is 70 (t-2).

To find what time they are at the same price, set the equations equal.

50t = 70 (t-2)

50t = 70t - 140

-20t = - 140

t=7

To find the amount of miles, substitute 7 into one equation.

50 (7) = 350 miles