1. Jim has a total of 50 coins. Some are nickels and some are dimes. Altogether he has $4.15. How many dimes and nickels does he have?
Let the number of nickels be n and the number of dimes be d.
n + d = 50
0.05*n + 0.10*d = 4.15
Solving the top equation for d:
d = 50 - n
Insert this into the bottom equation:
0.05*n + 0.10*[50 - n] = 4.15
0.05*n + 5.00 - 0.10*n = 4.15
-0.05*n = 4.15 - 5.00 = -0.85
n = (-0.85)/(-0.05) = 17
Thus d = 50 - 17 = 33
May 8th 2007, 06:56 PM
Originally Posted by poeticprincess
2. A sailboat travels 20 miles downstream in 3 hours. It returns in 4 hours. Find the speed of the sailboat in still water and the rate of the current.
Let the +x direction be the direction of the current. Let the distance the sailboat travels downstream be d = 20 miles. Let the speed of the boat in still water be v (with respect to the water.) Let the speed of the water be w (with respect to the ground.)
So the speed of the boat downstream with respect to the ground is v + w. So it covers the distance d in a time t given by:
d = (v + w)t --> t = 3 hours
When the boat moves upstream its speed with respect to the ground will be v - w. So it covers the distance d in a time T given by:
d = (v - w)T --> T = 4 hours