train problem?

Question

A train leaves Colorado Springs at 9:00 am bound for Boulder Colorado, 100 miles away. It travels at 50 mph and has to pick up passengers every 25 miles. Each stop takes 10 minutes, and after each stop, the increased passenger weight causes the train's speed to decrease by 10 percent. When does the train arrive in Boulder?

i'm having a little trouble with this word problem. Are there really only 3 stops to pick up people?

Answer 1

It arrives at the first station at 9:30, and leaves at 9:40. The new speed will be 50mph(0.9) = 45 mph.

So it takes 25miles/45mph = 33 minutes, 20 seconds to get to the next stop at 10:13:20, and leaves at 10:23:20. The new speed will be 45mph(0.9) = 40.5mph.

So it takes 25miles/40.5mph = 37 minutes, 2.22 seconds to get to the next stop at 11:00:22.22, and leaves at 11:10:22.22. The new speed will be 40.5mph(0.9) = 36.45mph

So the last leg of the trip should take 25 mi/36.45mph = 41 minutes, 9.136 seconds. So I think, if I didn't screw up, they'll arrive at 11:51:31.358 pm.

Answer 2

Yes, three stops: at the 25 mile mark, 50 mile mark and 75 mile mark. At the 100 mile mark, it's not a stop to pick up passenger like before, it's the end of the ride (make a diagram like a number line and you'll see).

It goes 50 mph for the first 25 miles, so that takes 1/2 hr. Add ten minutes at the first stop, we're now 40 min. out of Colorado Springs.
After that stop, it's 10% slower = going 45 mph for the next 25 miles, so that takes 33 min ... add that to the 40 min, the trip has taken 73 min. so far. Ten minutes at stop 2 brings us up to 83 min. since we left C.S.

After stop 2, train slows down to 40 mph (I'm using 10% of the original 50 mph speed for it to slow down. If it's 10% of the speed for the previous 25 miles, which is not exactly clearly given in the problem, you'd use 40.5 mph). It covers miles #50 to 75 in approximately 38 min, bringing us to the 121 minute mark, and making it 131 minutes since we left C.S. after stop #3.

Now the train's going 35mph for the final 25 miles. It covers that in about 43 minutes. Add that to the 131, and we're up to 174 min., or a total trip of two hours and 54 minutes, making it 11:54am if Boulder and Colo. Springs are in the same time zone, which they are.

For extra credit: what time would it say on the clock in the terminal on arrival if the 100 mile train trip as described above could be taken from Sterling, CO, traveling northeast, to somewhere around Roscoe, NE? :-)

Answer 3

yup, only 3 stops to consider here, as the ppl picked at colorado springs and at boulder is irrelevant.
50mph >> 25 miles in 30 mins.
1st stop : reached at 9:30 , leave at 9:40

speed down by 10 percent.. new speed: 0.9*50 = 45mph
next 25 miles covered in 25/45 * 60 = 33 +1/3 mins ie, 33 mins 20 secs

so 50-mile point (2nd stop) reached at 9:40 + 33mins 20 secs
and we leave it 10 mins later, at 10:23::20 (hr:min::sec format)

again speed down by 10 percent... of original speed, i hope?
so new speed = 0.8*50 = 40mph
now the 25 miles covered in 25/40*60 = 37.5 mins
& including 10-min wait at this (3rd) stop 10mins,
train leaves 3rd stop at 10:23::20 + 0:47::30 = 11:10::50 am

now speed again reduces to 70%, 0.7*50 = 35mph
last 25 miles covered in 25/35*60 = 42.8571 mins , ie, 42mins 51 secs (approx)
so time of reaching boulder: 11:10::50 + 0:42::51 = 11:53::41 am

this calculation is on the premise that speed reduction is relative to first speed (50mph). if the speed is reducing relative to prev speed (ie, before the passengers got on) then u'll have to change the speed calculations accordingly

Answer 4

It travels the first 25 miles in 25/50 = 1/2 hour
It travels the next 25 miles in 25/45 = 5/9 hour
It travel the next 25 miles in 25/40.5 = .617 hour
It travels the final 25 miles in 25/36.5 = .685 hour

Total train time = .5 +.555 +.617 + .685 = 2.357 hours
Total wait time = 3*10 = 30 minutes =.5 hour
Total travel time = 2.857 hours
= 2 hours 51.4 minutes
So train arrived at 11:51.4 AM

Answer 5

yes there are 3 stops, at 25miles, 50miles and 75miles.

to figure this out, just go systematically through the train ride:

(25/50)*60 + 10 + (25/(50-5))*60 + 10 + (25/(45-4.5))*60 + 10 + (25/(40.5-4.05))*60
=30 + 10 + 33.33 + 10 + 37.04 + 10 + 41.15
=171.52 minutes
= 2 hours, 52 minutes

so, the train would arrive at 11:52

Answer 6

Train reaches the first 25 mi stop in 30 min and waits for 10 min

now, for the next 25 mi, train's speed is 45 mph.

Train reaches second 25 mi stop in 33.33 min and waits for 10 min

now, for the next 25 mi, train's speed is 40.5 mph

Train reaches third 25 mi stop in 37.04 min and waits for 10 min

for last 25 mi, train's speed is 36.45 mph so it takes 41.15 min to cover that distance.

Add all times and you will get required answer.

Answer 7

v=d/t
---------------------------------
first 25
t=d/v=25/50=0.5h
-------------------------
next 25

50-0.10(50)=45

t=25/45=0.56h
----------------------------
next 25

45-0.10(45)=40.5

t=25/40.5=0.62h
----------------------------------
final 25

40.5-0.10(40.5)=36.45

t=25/36.45=0.69h
----------------------------------

Total Distance=25+25+25+25=100

Total Time= 0.5h+0.56h+0.62+0.69=2.37h

2.37h(60min)=142.2min

or 2hours and 22.2 min

they will arrive in Boulder Colorado 2 hours and 22.2 min after departing at 9:00 am from colorado, so they will arrive in Boulder Colorado 11hours:22min:2seconds in terms of Colorado time.