Having trouble with another word problem. Help is greatly appreciated!
The word problem is below.
An insurance representative traveled 735 miles by commercial jet and then an additional 105 miles by helicopter. The rate of the jet was four times the rate of the helicopter. The entire trip took 2.2 hours. Find the rate of the jet.
Let “J” be the speed of the jet in miles per hour. Then the speed of the helicopter was J/4 miles per hour. Since speed is distance over time (s=d/t), that means time is distance over speed (t=d/s). So the time on jet was 735/J and the time on helicopter was 105/(J/4). The total trip was 2.2 hours, so:
(735/J) + (105/(J/4)) = 2.2
Solve this for J. (Hint: change the 105/(J/4) to (4*105)/J, then multiply both sides by J.)
d=vt; v1= jet v2=heli
t1 + t2 = 2.2 hrs
d1/v1 + d2/v2 = 2.2 hrs
735/4v2 + 105/v2 = 2.2 ==> multiply both sides with 4v2
735 + 105(4) = 2.2 ( 4v2)
735 + 420 = 8.8v2
8.8v2 = 1155
v2 = 131.25 miles/hr
v1 = 4(v2) = 4(131.25) = 525 miles/hour