The average speed of a jet is 100km/h faster than a cargo plane. To travel 1400km, the cargo plane requires 25% more time than the jet. Find the average speed of the jet.
This is the formula I figured out so far.
V(average)=V(jet)-V(cargo
100km/h= d/t - d/t
100= [1400km/x] - [1400/(.25x+x)]
But from here I don't know what to do..
Call the speeds j and c.
j - c = 100 -> j = 100 + c
(100 + c) = 5c / 4 (from the "25% faster")
Solve for c.
Creating a chart makes these kind of problems real easy
3 columns: Distance, Rate , Time and remember D = RT
2 rows: jet and cargo plane
-----D-----R------T
Jet 1400 -- x+100 -- 1400/(x+100)
Cargo 1400 ----x -- 1400/x
(hope the spacing comes out halfdecent.)
It said the time of the cargo plane is 25% more than the time of the jet, so
1400/x = 1.25(1400)/(x+100)
1400/x = 1750/(x+100)
cross-multiply
1750x = 1400x + 140000
x = 400
So the cargo's speed is 400 km/h and the jet goes 500 km/h
check:
time of jet = 1400/500 = 2.8 hours
time of cargo = 1400/400 = 3.5
What is 25% of 2.8 added to 2.8 ?
YUP!!!!
To solve the problem, we can start by assigning variables to the unknowns in the problem. Let's say the average speed of the cargo plane is V(cargo) km/h and the average speed of the jet is V(jet) km/h.
Given that the average speed of the jet is 100 km/h faster than the cargo plane, we can write the first equation as:
V(jet) = V(cargo) + 100
We also know that the cargo plane requires 25% more time than the jet to travel a distance of 1400 km. Let's calculate the time taken by each:
Time taken by the jet = Distance / Speed = 1400 / V(jet)
Time taken by the cargo plane = Distance / Speed = 1400 / V(cargo)
According to the problem, the cargo plane requires 25% more time than the jet, so we can write the second equation as:
1400 / V(cargo) = 1.25 * (1400 / V(jet))
Now, we can substitute the value of V(jet) from the first equation into the second equation to eliminate one variable:
1400 / V(cargo) = 1.25 * (1400 / (V(cargo) + 100))
To continue solving, we can cross multiply and rearrange the equation to isolate V(cargo):
1400 * (V(cargo) + 100) = 1.25 * 1400 * V(cargo)
Expanding both sides of the equation:
1400 * V(cargo) + 140000 = 1750 * V(cargo)
Rearranging the equation:
1400 * V(cargo) - 1750 * V(cargo) = -140000
Combining like terms:
-350 * V(cargo) = -140000
Dividing both sides of the equation by -350:
V(cargo) = -140000 / -350 = 400 km/h
Therefore, the average speed of the cargo plane is 400 km/h.
To find the average speed of the jet, we can substitute the value of V(cargo) into the first equation:
V(jet) = V(cargo) + 100
V(jet) = 400 + 100 = 500 km/h
So, the average speed of the jet is 500 km/h.