Pat L.

asked • 02/01/15# Average speeds

An automobile averaged 40 mph for part of a trip and 50 mph for the remainder. If the 5-hour trip covered 210 miles, for how long did the car average 40 mph?

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## 2 Answers By Expert Tutors

Jacoby B. answered • 02/02/15

Tutor

5.0
(158)
Math, Science and Test Prep Tutor

We need to have a good understanding of two (2) core concepts: Average speed = Total Distance Traveled/ Total Time Taken

And,

the Sum Product Rule: a(b) + c(b) = d(b)

By rearranging the rate equation we get: rate * time = distance

We know the two (2) times are as follows from the given information:

T1 = t

T2 = 5-t (for the remaining portion of the trip)

So, we can infer:

40*T1 + 50*T2 = 210 miles traveled

40t + 50(5 - t) = 210

40t + 250 - 50t = 210

-10t = -40

t = 4 = T1

T2 = 1

Faraz R. answered • 02/01/15

Tutor

4.9
(565)
TOP RANKED AP CALCULUS, CHEMISTRY, PHYSICS TUTOR.GET A 5 ON YOUR AP!!!

x is number of hours traveled at 40 mph

5-x is number of hours traveled at 50 mph

40x + 50(5-x) = 210

40x + 250 -50x = 210

-10x +250=210

Take 250 over by subtracting from both sides

-10x = -40

x = 4 at 40 mph

1 hour at 50 mph

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