SOLUTION: A car took 5 hours to travel from town A to town B. A bus took 9 hrs to travel the same route. both the car and bus started at the same time. if the speed of the car was 90km/h, ho

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Question 1164834: A car took 5 hours to travel from town A to town B. A bus took 9 hrs to travel the same route. both the car and bus started at the same time. if the speed of the car was 90km/h, how much faster did the bus need to travel in order to reach town B 1hr and 36 min earlier than the expected arrival time. if it could only increase it's speed after 3/5 of the journey?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
rate * time = distance.
time = distance / rate
rate = distance / time
rate is the distance traveled in a specified period of time.
that's the same as speed in this problem.

the car took 5 hours to travel from town A to town B.
the speed of the car was 90 kilometers per hour.
the distance was therefore 5 * 90 = 450 kilometers.

the bus took 9 hours to travel the same distance.
the speed of the bus was therefore 450/9 = 50 kilometers per hour.

you want the bus to go from town A to town B 1 hour and 36 minutes earlier than its scheduled time.
its scheduled time was 9 hours.
1 hour and 36 minutes earlier is equal to 1 + 36/60 = 1.6 hours earlier.
9 hour minus 1.6 hours is equal to 7.4 hours.
the new scheduled time would need to be 7.4 hours rather than 9 hours so that the bus would go from town A to town B 1 hours and 36 minutes ahead of schedule.

to go from town A to town B in 7.4 hours, the bus would have to travel at a rate of 450 / 7.4 = 60.81081082 kilometers per hour rounded to 8 decimal digits.
that would be an increase in speed of 10.81081082 kilometers per hour rouned to 8 decimal digits.

if the bus could only increase its speed after 3/5 of the journey was completed, then the bus could only increase speed after 3/5 * 450 = 270 kilometers were completed.
that leaves 180 kilometers in which the bus could increase its speed.

270 kilometers at 50 kilometers takes 270/50 = 5.4 hours.
to complete the whole trip in 7.4 hours, then the bus has 7.4 - 5.4 = 2 hours to complete 180 kilometers.
to do that, the bus would need to travel 180 / 2 = 90 kilometers per hour.
that would be an increase of 90 - 50 = 40 kilometers per hour.

to confirm these values are good. do the following.

450 kilometers completed in 7.4 hours equals a speed of 450 / 7.4 = 60.81081081 kilometers per hour for the whole trip.
that's what we calculated before, so that's good.

450 kilometers at a speed of 50 kilometers per hour for the first 270 kilometers and at a speed of 90 kilometers per hour for the last 180 kilometers would take a total of 270 / 50 = 5.4 hours for the first 270 kilometers plus 180 / 90 = 2 hours for the last 180 kilometers for a total of 7.4 hours to cover the entire 450 kilometer distance.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A car took 5 hours to travel from town A to town B. A bus took 9 hrs to travel the same route. both the car and bus started at the same time. if the speed of the car was 90km/h, how much faster did the bus need to travel in order to reach town B 1hr and 36 min earlier than the expected arrival time. if it could only increase it's speed after 3/5 of the journey?
Since car takes 5 hours to reach B, @ 90 km/h, distance from A to B = 5(90) = 450 km


Since bus takes 5 hours to reach B, a distance of 450 km, the bus' speed = matrix%281%2C4%2C+450%2F9%2C+%22=%22%2C+50%2C+%22km%2Fh%22%29

Travelling 3%2F5 of the distance, the bus must travel matrix%281%2C6%2C+3%2F5%2C+of%2C+450%2C+%22or%22%2C+270%2C+km%29. This means that the bus needs to travel another 180 (450 - 270) km to get to B

The bus traveled 270 km from A, in matrix%281%2C4%2C+270%2F50%2C+%22=%22%2C+27%2F5%2C+hours%29. Therefore, it needed another matrix%281%2C4%2C+9+-+27%2F5%2C+or%2C+18%2F5%2C+hours%29 to get to B on time

However, since it'd need to get to B matrix%281%2C6%2C+1%2636%2F60%2C+or%2C+1%263%2F5%2C+%22=%22%2C+8%2F5%2C+hours%29 sooner, then it'd need to travel for matrix%281%2C6%2C+18%2F5+-+8%2F5%2C+%22=%22%2C+10%2F5%2C+%22=%22%2C+2%2C+hrs%29

Traveling the remaining 180 km to B, in 2 hours means that the bus would need to travel at a speed of matrix%281%2C4%2C+180%2F2%2C+%22or%22%2C+90%2C+%22km%2Fh%22%29

Hence, the bus would need to travel matrix%281%2C4%2C+%2290+-+50%2C%22%2C+or%2C+40%2C+%22km%2Fh%22%29%29 more to get to B, 1 hour and 36 minutes earlier than planned.