Louise K. answered • 03/09/20

Certified Teacher, Experienced Tutor, many subjects, especially math

ok, let's break this down. First, we identify three variables:

D = downhill speed U = uphill speed L = speed on level ground

They tell us D = 120 miles per hour.

Next, we know that D = 2 U. Using our algebra skills, that means that 120 = 2 U or 60 = U

Next, they say that it goes uphill at 2/3 of the level speed, so 2/3 L = U We know that U=60 so 2/3 L = 60. We can use the reciprocal shortcut here and multiply both sides by 3/2 (or multiply each side by 3 and then divide each side by 2 if you don't use the reciprocal shortcut, it is the same result). That means that L = (3/2)60 = 90 miles per hour

We need to go 45 miles on level ground. 45 is half of 90, so we are traveling for a half hour.