Cindy left by plane to visit her mother in Hartford 420km aw

Cindy left by plane to visit her mother in Hartford, 420km away. Fifteen minutes later, her mother left to meet her at the airport. She drove the 20 km to the airport 40 km per hr, arriving just as the plane taxied in. What was the speed of the plane?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=speed of the plane
When Cindy\'s mother left the plane had already travelled (15/60)*r km and it took Cindy\'s mother 20/40=1/2 hr to get to the airport. During this time the plane travelled another (1/2)*r km and we are told that these two distances that the plane travelled equals 420 km, so:
(15/60)r + (1/2)r=420 or
(1/4)r+(2/4)r=420 and
(3/4)r=420 multiply each side by 4
3r=1680
r=560 km/hr--------------------------speed of the plane