Question 1124609: Courtney rides her bike then the bus and finally the train to visit her aunt. She rides her bike at 6 mph. The bus travels at 30 mph while the train carries her at 140 mph. She rides the train for 57 minutes less than she rides the bus. She traveled 363 miles in 5 hours 21 minutes. How long was she riding her bike and reading on the bus?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39615)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Courtney rides her bike then the bus and finally the train to visit her aunt.
She rides her bike at 6 mph.
The bus travels at 30 mph while the train carries her at 140 mph.
She rides the train for 57 minutes less than she rides the bus.
She traveled 363 miles in 5 hours 21 minutes.
How long was she riding her bike and riding on the bus?
:
change 5 hr 21 min to hrs: 5 + 21/60 = 5.35 hrs
:
let b = time riding the bike
then
6b = distance on the bike
:
let c = time riding the bus
then
30c = distance on the bus
:
let t = time on the train
then
140t = distance on the train
:
total dist equation
6b + 30c + 140t = 363 mi
:
total time equation
b + c + t = 5.35
:
"She rides the train for 57 minutes less than she rides the bus"
c - 57 min = t
change 57 min to hrs: 57/60
c = t + .95
:
in the first equation replace c with (t+.95)
6b + 30(t+.95) + 140t = 363
6b + 30t + 28.5 + 140t = 363
6b + 170t = 363 - 28.5
6b + 170t = 334.5
:
Do the same in the 2nd equation
b + (t+.95) + t = 5.35
b + 2t = 5.35 - .95
b + 2t = 4.4
b = -2t + 4.4
:
Replace b with (-2t+4.4) in 6b + 170t = 334.5
6(-2t+4.4) + 170t = 334.5
-12t + 26.4 + 170t = 334.5
158t = 334.5 - 26.4
158t = 308.1
t = 308.1/158
t = 1.95 hrs on the train
:
find how long on the bike
b = -2(1.95) + 4.4
b = 3.9 + 4.4
b = .5 hrs on the bike
:
Now how long on the bus
.5 + c + 1.95 = 5.35
c = 5.35 - 2.45
c = 2.9 hrs on the bus
:
"How long was she riding her bike and riding on the bus?
.5 hrs and 2.9 hrs, that is
30 min on the bike
2 hr 54 min on the bus
;
:
These solutions were not integers so checked this using the matrix feature on my Ti83
1, 1, 1, 5.35
6, 30, 140, 363
0, 1 - 1, .95
It was gratifying to see that their solutions agreed with mine: .5, 2.9, 1.95
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