SOLUTION: Wendy took a trip from city A to city B, a distance of 910 mi. She traveled part of the way by bus, which arrived at the train station just in time for Wendy to complete her journe

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Question 993957: Wendy took a trip from city A to city B, a distance of 910 mi. 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 30 mi/h, and the train averaged 115 mi/h. The entire trip took
10 1/2h.
How long did Wendy spend on the train?
Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles she traveled by bus
+910+-+d+ = distance in miles she traveled by train
Let +t+ = time in hrs she spent on bus
+10.5+-+t+ = time in hrs she spent on train
-----------------------------------------
Equation for bus:
(1) +d+=+30t+
Equation for train:
(2) +910+-+d+=+115%2A%28+10.5+-+t+%29+
-----------------------------
Substitute (1) into (2)
(2) +910+-+30t+=+115%2A%28+10.5+-+t+%29+
(2) +910+-+30t+=+1207.5+-+115t+
(2) +85t+=+297.5+
(2) +t+=+3.5+
and
+10.5+-+t+=+10.5+-+3.5+
+10.5+-+t+=+7+
Wendy spent 7 hrs on the train
--------------------------
check:
(1) +d+=+30t+
(1) +d+=+30%2A3.5+
(1) +d+=+105+
and
(2) +910+-+d+=+115%2A%28+10.5+-+t+%29+
(2) +910+-+d+=+115%2A%28+10.5+-+3.5+%29+
(2) +910+-+d+=+805+
(2) +d+=+105+
OK

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Wendy took a trip from city A to city B, a distance of 910 mi. 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 30 mi/h, and the train averaged 115 mi/h. The entire trip took
10 1/2h.
How long did Wendy spend on the train?
let x=distance Wendy traveled by bus
910-x=distance Wendy traveled by train
distance/speed=travel time
x/30+(910-x)/115=10.5
lcd: (30)(115)
115x+30(910-x)=10.5* (30)(115)
115x+27300-30x=36225
85x=8925
x=105
910-x=805=(distance Wendy traveled by train)
805/115=7
How long did Wendy spend on the train? 7 hrs