# distance problems?

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

2. 2 cyclist, 90mi apart, start riding toward eachother at the same time. Once cycles twice as fast as the other. If they meet 2 h later, at what average speed is each cyclist traveling?

3. A pilot flew a jet from Montreal to LA, a distance of 2500 mi. on the return trip the average speed was 20% faster than the outbound speed. the round trip took 9 h 10min. What was the speed from Montreal to LA?

Relevance

1. W traveled B miles by bus @ 40mph and T miles by train @ 60 mph.

B+T = 300 --> the total miles traveled

B/40 + T/60 = 5.5 --> the total time traveled.

120B/40 + 120T/60 = 120*5.5

3B+2T = 660

2B + 2T = 600

B = 60

T = 240

So let's check.

60 miles at 40mph took 60/40 hours = 1.5 hours

240 miles at 60 mph took 240/60 hours = 4 hours

So the total distance is 300 miles and the total time is 5.5 hours.

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2. cyclist 1 travels x mph and cyclist 2 travels 2x mph and their average speed is x+2x=3x mph.

If they meet in 2 hours then their average combined speed is 90/2 = 45 mph

3x = 45 --> x=15

so cyclist 1 travels at 15 mph and cyclist 2 traves at 30 mph.

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3. 9h 10m = 9 1/6h = 55/6 hours.

the initial speed is x and the return speed is 1.2x so

2500/x + 2500/(1.2x) = 55/6

2500*1.2 + 2500 = 55/6*1.2x

5500 = 11x

x = 550

So the trip to LA was flown at 550 mph.

• Anonymous

1) 60t+40b=300-----b=(300-60t)/40

t+b=5.5

t+(300-60t)/40=5.5

40t+300-60t=220

-20t=-80

t=4 hours

just set up two equations and then substitute and solve