Problema Solution
A jet plane, flying 85 mph faster than a propeller plane, travels 3400 miles in 2 hours less time than the propeller plane takes to fly the same distance. How fast does each plane fly?
Answer provided by our tutors
distance = speed * time
speed = distance / time
let 't' represent the time flown by the jet, then 't+2' represents the time flown by the propeller plane
let 'v' represent the velocity of the propeller plane, then 'v+85' represents the velocity of the jet
3400 = t(v+85)
3400 = (t+2)v, so v = 3400(t+2)
substituting 'v' with '3400/(t+2)' in the first equation:
3400 = t((3400/(t+2)) + 85)
solving for 't' we have a positive value of t=8
8+2 = 10
now we solve for speed:
for the jet, speed = 3400/8 = 425
for the propeller plane, speed = 3400/10 = 340
check: 425 - 340 = 85
the jet flies 8 hours at a speed of 425 mph
the propeller plane flies 10 hours at a speed of 340 mph