Math word problem regarding miles per hour

Question

A car went 210 miles in six hours, traveling part of the time at 30 miles per hour on some back roads. And part of the time at 45 mph on some primary roads until the driver is stopped by police.  How long did the car travel at each speed?

Answer 1

Hi Antonio

 

Well I like this question.  Remember that Distance = Rate multiplied by Time.

 

You know the car went 210 miles in 6 hours and you have 2 different rates for that overall time.  One is 30 mph and one is 45 mph.  If the time you spent going 30 mph is T then the time you spent going 45 mph is 6 - T right?.  That gives us an equation that looks like this:

 

30T + 45(6-T) = 210

 

Solve for T

 

30T + 270 - 45T = 210

-15T                  = -60

                       T = 4

 

Let's see if that makes sense, if you were going 30 mph for 4 hours you would have gone 120 miles.  Then if you went 45 mph for 2 hours you went another 90 miles for a total of 210 miles.  Seems ok to me, let me know what you think.

 

All the best,

 

Lori