Can you help me with a word problem?

Question

An F-100 plane and a Toyota truck leave the same town at sunrise and head for a town 450 miles away. The speed of the plane is three times the speed of the truck, and the plane arrives 6 hours ahead of the truck. Find the speed of the truck.

Answer 1

Hi there. You can think about it this way. The plane is 3x as fast as the truck, so by the time the plane has reached the destination (450 miles away) the truck has traveled 1/3 of the distance, that is 150 miles. The truck will complete the rest of the travel (300 miles) in 6 hours and therefore its speed is 300 mi/6 hrs = 50 mph. Hope that helps.

Answer 2

if you assume the speed is constant and a direct route (straight line) is taken, and speed = s for the truck, and let time the plane takes = t (hours),

speed = distance / time

for plane, 3s = 450 / t
for truck, s = 450 / (t+6)

multiplying the second equation by 3 and subtracting,

[ 450 / t ] - [ 1350 / (t+6) ] = 0

so, 3t / (t+6) - 1 = 0, so, 2t/3 = 2, so, t = 3 hours.

so, the speed of the truck is, s = 450 / (3 + 6) = 450 / 9 = 50 m/p/h

Answer 3

t = time for truck to travel 450 miles
s = speed of truck

t - t/3 = 6 hours
(2/3)t = 6
t = 6(3/2) = 9 hours

s = 450 miles/9 hours = 50 miles/hour

Answer 4

S=450 miles Vt velocity truck etc, T the time taken

T= S/Vt=S/Vp + 6
=S/3Vt +6 ( Vp=3Vt)
(S/Vt)(3Vt)=(3Vt)(S/3Vt) +6(3Vt)
3S=S+18Vt
2S=18Vt
Vt=1/9S = 1/9(450) = 50 miles per hour

Answer 5

huh