Homework Help: math(rational functions application)

Posted by jane on Thursday, October 22, 2009 at 6:23pm.

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..

math(rational functions application) - jim, Thursday, October 22, 2009 at 6:34pm
Call the speeds j and c.

j - c = 100 -> j = 100 + c

(100 + c) = 5c / 4 (from the "25% faster")

Solve for c.
math(rational functions application) - Reiny, Thursday, October 22, 2009 at 6:37pm
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!!!!

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