Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-During a hurricane evacuation from the east coast of Georgia, a family traveled 240 miles west. For part of the trip, they averaged 50 mph, but as the congestion got bad, they had to slow to 10 mph. If the total time of travel
Was 9 hours, how many miles did they drive at the reduced speed?
A) 57.5 miles
B) 62.5 miles
C) 47.5 miles
D) 52.5 miles

Question

Quizplus · Accepted Answer

Let x be the number of hours they drove at 50 mph and y be the number of hours they drove at 10 mph.

We know that:

x + y = 9 (total time)

We also know that they traveled a total of 240 miles:

50x + 10y = 240

We can use the first equation to solve for one variable in terms of the other:

x = 9 - y

Substituting this into the second equation:

50(9 - y) + 10y = 240

Expanding and simplifying:

450 - 50y + 10y = 240

-40y = -210

y = 5.25

So they drove at 10 mph for 5.25 hours.

To find the distance traveled at this speed:

distance = speed × time

distance = 10 × 5.25

distance = 52.5 miles

Therefore, the answer is D (52.5 miles).

Set Up an Equation That Can Be Used to Solve