Algebra 2 word problem help?
1) You and a college roommate travel to your respective hometowns in the same amount of time. You travel a total of 210 miles and your roommate travels 190 miles. Your friend's speed is 6 mph lower than yours. What is your and your friend's average speed?
2) A boat travels at a speed of 20mph in still water. The boat travels at a speed of 48 mph upstream and then returns to the starting point in a total of 5 hours. Find the speed of the current.
I know the answer is 4mph but I don't know how to find it.
Update:That's what I thought, too when I tried to work the problem, but that's exactly how it appeared in my book. Perhaps it is a typo or something. Thank you for your help, though.
Comments
Distance equals rate times time. Use y for your rate and y - 6 for your roommate's speed.
210 = T * y [you cover 210 miles at your rate in some amount of time]
190 = T * (y -6) [your roommate covers 190 miles at your rate minus 6 mph in the same amount of time]
Solve both equations for T:
T = 210 / y
T = 190 / (y - 6)
Set the two right sides equal to each other:
210 / y = 190 / (y - 6)
Cross-multiply:
210(y - 6) = 190y
Multiply out the left side:
210y - 1260 = 190y
Subtract 190y from and add 1260 to both sides:
20y = 1260
Divide both sides by 20:
y = 1260 / 20 = 63
Your speed is 63 mph; your roommate's speed is 6 mph slower at 57 mph.
Upstream speed is 20 mph minus the speed of the current. Something's wrong with the way you've stated the question. The 48 mph upstream speed has to be wrong.