"Charlie biked 15 minutes from home to school and then walked 12 minutes to the pizza place near his house. This trip was 3.6 miles in total."
We will call the speed he rides his bike at "b" and the speed he walks at "w".
It follows that the sum of 15 minutes at biking speed and 12 minutes at walking speed is the total distance of 3.6 miles. But watch for the unit conversion from minutes to hours:
3.6 = 1/4 b + 1/5 w
"His rate on his bike is 3 miles per hour less than 5 times his walking rate."
As "b" is "his rate on his bike" and "w" is "his walking rate", it follows that 5 times "w" - 3 is the same as "b".
b = 5w - 3
Now we can substitute "b" in the first equation with "5w - 3" from this one and solve for "w":
3.6 = 1/4 (5w - 3) + 1/5 w | distribute 15 & find commons denominator
3.6 = 25/20 w - 3/4 + 4/20 w | combine like terms
3.6 = 29/20 w - 3/4 | +3/4 (or 0.75)
4.35 = 29/20 w | / 29/20 (or * 20/29)
w = 3 mph
Now replace "w" in the second of our initial equations and solve for "b":
b = 5(3) - 3
b = 15 - 3
b = 12 mph
Now prove by inserting both into the initial equation:
3.6 = 1/4 b + 1/5 w
3.6 = 1/4 (12) + 1/5 (3)
3.6 = 3 + .6 <== correct
