SOLUTION: I have two problems that I can't solve. Thank you! 1.Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph

Question 277553: I have two problems that I can't solve. Thank you!
1.Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph and returns at 2 kph, how far will he have paddled the canoe?
2.A car and a motorcycle whose average rates are in the ratio of 4:5 travel a distance of 160 miles. If the motorcycle travels 1/2 hour less than the car, find the average rate of each.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.Roger Waters can scrape up just enough money to rent a canoe for 1 hour and 30 minutes. If he paddles out on a lake at 4 kph and returns at 2 kph, how far will he have paddled the canoe?
----
Out DATA:
rate = 4km/h ; time = x hrs ; distance = rt = 4x km
---------------
In DATA:
rate = 2 km/h ; time = 1.5-x hrs ; distance = 2(1.5-x) = 3-2x km
-------------------
Equation:
distance out = distance back
4x = 3-2x
6x = 3
x = 1/2 km
-------------------
Distance paddled = 2x = 1 km
=================================

2.A car and a motorcycle whose average rates are in the ratio of 4:5 travel a distance of 160 miles. If the motorcycle travels 1/2 hour less than the car, find the average rate of each.
---
Car data:
rate = 4x mph ; distance = 160 mi ; time = d/r = 160/4x = 40/x hrs
-------------------
Cycle DATA:
rate = 5x mph ; distance = 160 mi ; time = d/r = 160/5x = 32/x hrs
----------------------
Equation:
car time - cycle time = 1/2
40/x - 32/x = 1/2
Multiply thru by 2x to get:
80 - 64 = x
x = 16
---
Car Rate = 4*16 = 64 mph
Cycle Rate + 5*16 = 80 mph
===================================
Cheers,
Stan H.
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