SOLUTION: One hour out of the station, a train engine develops trouble that slows the train to 3/5 of its average speed to the time of the failure. Continuing at this reduces speed,it reache
Algebra.Com
Question 69535: One hour out of the station, a train engine develops trouble that slows the train to 3/5 of its average speed to the time of the failure. Continuing at this reduces speed,it reaches its destination two hours late. Had the trouble occurred 50 miles beyond, the delay would have been reduced by 40 minutes. Find the distance from station to the destination.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
ne hour out of the station, a train engine develops trouble that slows the train to 3/5 of its average speed to the time of the failure. Continuing at this reduces speed,it reaches its destination two hours late. Had the trouble occurred 50 miles beyond, the delay would have been reduced by 40 minutes. Find the distance from station to the destination.
Let T = normal time it takes to make the trip
Let D = distance of the trip
Let S = normal speed
Then normal Time = D/S
Distance = S*T
Let (3/5) = .6
Let 40 min = .67 hrs
:
Two equations to go the same distance
:
Eq1:
S*T = D; normal trip
:
Substitute S*T for D in eq 2
:
Eq2:
1S + .6S(T+2-1) = S*T
Divide equation by S
1 + .6(T+1) = T
1 + .6T + .6 = T
.6T - T = -.6 - 1
-.4T = -1.6
T = -1.6/-.4
T = + 4 hrs is the normal time to take the trip
:
We then also know that D = 4S
:
Equation for the addition 50 mi at normal speed:
:
1S + 50 + .6S(4 + 2 - 1 - .67) = D
1S + .6S(4.33) = D - 50
Substitute 4S for D, multiply what's inside the brackets:
1S + 2.6S = 4S - 50
3.6S - 4S = - 50
-.4S = - 50
S = -50/-.4
S = 125 mph is normal speed
:
.6 * 125 = 75 mph is reduced speed
:
Distance = 4(125) = 500 miles is the trip
:
Check:
Normal speed for 1 hr + .6 normal speed for 5 hrs = 6 hrs for the trip
1(125) + 5(75) = 500 miles
:
Check using additional 50 mi at normal speed
1(125) + 50 + (5 - .67)* 75 =
125 + 50 + 325 = 500 mi
:
This was a toughie, hope it makes sense to you.
RELATED QUESTIONS
A train travels 240 miles at a speed of 80 miles/hour. On the way back the train slows... (answered by ewatrrr)
1. If the average speed of a train between two stations is 30 miles per hour and the two... (answered by macston)
The distance between train station A and train station B is 180 kilometers. Train station (answered by stanbon)
In the middle of its journey from station A to station B, a train was held up for 10... (answered by ankor@dixie-net.com)
I have puzzled on this one a while - seems like I have two variables and two equations to (answered by ankor@dixie-net.com)
Train A leaves the station traveling a constant 35 miles per hour. One hour later, Train... (answered by ikleyn)
Two trains left a station at the same time and traveled in opposite directions. One train (answered by mananth)
A man misses the train by 2 minutes if he walks to the the station at an average speed of (answered by jorel1380)
A train travelling at an average speed of 53 km per hour. At this rate of speed, the... (answered by Alan3354)