Question

Wendy took a trip from Davenport to Omaha, a distance of 300mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journey by train. The bus averaged 40mi/h and the train 60mi/h. The entire trip took 5-1/2 hours. How long did Wendy spend on the train?

Answer 1

let x = time she spent on the bus
y = time she spent on the train

according to the formula speed = distance/time, we can conclude that distance = speed x time

so

40x is the distance she traveled by bus and 60y is the distance she traveled by train. the total of this should be the total distance so

40x + 60y = 300

then like i said x is the time spent on the bus and y is the time spent in the train. so the total of this should be the total time so

x + y = 5 1/2 or simply

x + y = 11/2

we can simplify that further by multiplying all terms by 2

2x + 2y = 11

so now we have a system of equations:

40x + 60y = 300
2x + 2y = 11

we are looking for y (the time she spent on the train) so we eliminate x by multiplying the second equation by -20 then add the equations

40x + 60y = 300
-40x -40y = -220
==========
0x + 20y = 80

20y = 80

divide both sides by 20

y = 80/20

simplify

y = 4 hours

does that help?

Answer 2

YES! thank you so much!

Answer 3

welcome