Question 920399: a speedy river barge bound for New Orleans leaves Baton Rouge at 9:00 AM and travels at a speed of 10 mph. A rail transport freight train also bound for New Orleans leaves Baton Rouge at 1;30 PM on the same day. The train travels at 25 MPH and the river barge travels at 10 MPH. Both the barge and train will travel 100 miles to reach New Orleans. a) how far will the train travel before catching up to the barge? b) which shipment will reach New Orleans first? What time? c) If both shipments take an hour to unload before heading back to Baton Rouge, what is the earliest time that either one of the companies can begin to load grain to ship to Baton Rouge?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you want to convert everything to hours so that all subsequent calculations are easier to perform and consistent with each other.
the barge leaves at 9:00 am so that would be at 9 hours past midnight.
the train leaves at 1:30 pm so that would be at 13.5 hours past midnight.
the train is therefore leaving 4.5 hours after the barge.
the train will catch up to the barge when the distance that both have traveled is the same.
we'll call that d.
the basic formula to use is r*t = d, where r = rate and t = time and d = distance.
for the barge, that formula becomes 10*t = d
for the train, that formula becomes 25*(t-4.5) = d
since d is the same for both, then we get:
10*t = 25*(t-4.5)
we solve for t in this equation to get t = 7.5
when t = 7.5, the barge will have traveled 10*7.5 = 75 miles.
when t - 4.5 = 7.5 - 4.5 = 3, the train will have traveled 3 * 25 = 75 miles.
the train catches up to the barge after it has traveled 3 hours.
there are still 25 more miles to go to get to new orleans.
the barge will cover that in 2.5 hours, traveling at 10 miles per hour.
the train will cover that in 1 hour, traveling at 25 miles per hour.
the train will reach new orleans ahead of the barge.
the train will reach new orleans at 13.5 + 3 + 1 = 17.5 hours past the previous midnight.
the barge will reach new orleans at 9 + 7.5 + 2.5 = 19 hours past the previous midnight.
the train will therefore arrive at new orleans at 5:30 pm.
the barge will therefore arrive at new orleans at 7:00 pm.
add 1 hour to each of these for the time to unload each and you get:
the train will be ready to go back to baton route at 6:30 pm.
the barge will be ready to go back to baton rouge at 8:00 pm.
the solution to your questions are:
a) how far will the train travel before catching up to the barge?
75 miles.
b) which shipment will reach New Orleans first?
the train will reach new orleans first.
What time?
the train will reach new orleans at 5:30 pm.
c) If both shipments take an hour to unload before heading back to Baton Rouge, what is the earliest time that either one of the companies can begin to load grain to ship to Baton Rouge?
the train can begin to load grain to ship to baton rouge at 6:30 pm.
the barge can begin to load grain to ship to baton route at 8:00 pm.
the earliest time that either can begin to load grain to ship back to baton rouge is therefore 6:30 pm.
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