How far along this route is Paul’s house from the theater?

Question

Paul walks at a pace of 2kph to the theater and watches movie for 2 hours and 12 minutes. He rides back home,taking same route on a bus that travels at a rate of 30kph. The entire trip takes 7 hours. How far along this route is Paul’s house from the theater?

Answer 1

Total time is 7 hours, but the travel time is the part that can lead to the answer; the distance from Paul's house to the theater.

2hrs 12 min = 2 1/5 hrs.

Travel time is 7 - 2 1/5 = 4 4/5 hrs (4.8 hrs)

Total travel time is 4.8 = walk time + bus time. Walk rate is 2 km/hr; bus rate is 30 km/hr. The distance for the trip in each direction is D.

Dist = rate x time, so time = dist/rate

4.8 = D/2 + D/30 Common denom is 30

4.8 = (15D + 1D)/30

144 = 16D

D = 144/16 = 9 km.



Check: Walk time 9/2 hr + movie time 2 1/5 hr + bus time 9/30

4.5 + 2.2 + 0.3 = 7.0 hrs (easier to use decimals to add)

Answer 2

Answer 3

2 km/hr, 2 1/5 hour stop

goes back at 30 km/hr

both ways plus the stop take 7 hours

both ways without the stop take 7-2 1/5 = 4 4/5 hours = 4.8 hours

30x =2(4.8-x) = 9.6 -2x

32x = 9.6

x = 9.6/32 = 4.8/16 = 1.2/4 = .3 hours = .3(60) = 18 minutes on the bus

30(.3) = speed times time = distance = 9 kilometers one way

2(4.8-.3)=2(4.5)= 9 kilometers back

4 1/2 hours walking