Average speeds

Question

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?

Answer 1

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

 

 

 

Answer 2

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