SOLUTION: Two friends plan to meet at a restaurant for lunch. They both leave their homes at 11:30 A.M. and between the two of them, they drive a total of 37.5 mi. Lynn drives in from a ne

Algebra ->  College  -> Linear Algebra -> SOLUTION: Two friends plan to meet at a restaurant for lunch. They both leave their homes at 11:30 A.M. and between the two of them, they drive a total of 37.5 mi. Lynn drives in from a ne      Log On


   

Question 1137086: Two friends plan to meet at a restaurant for
lunch. They both leave their homes at 11:30 A.M. and between the two of them, they drive a total of 37.5 mi. Lynn drives in from a neighboring town and averages 15 mph faster than her friend Linda. If they meet at noon, find the average driving speed for each.
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Linda:
Distance = d = 0.5r
Rate = r
Time = 0.5

Lynn:
Distance = 37.5 - d = 37.5 - 0.5r
Rate = r + 15
Time = 0.5

r + 15 = (37.5 - 0.5r)/0.5

0.5(r + 15) = 37.5 - 0.5r

0.5r + 7.5 = 37.5 - 0.5r

r = 30

Linda:
Rate = r = 30 mph

Lynn:
Rate = r + 15 = 45 mph

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Solve using logical reasoning; algebra is not required. (Unless, of course, this is for an algebra course, where an algebraic solution IS required...!)

Together, the two of them covered 37.5 miles in half an hour; their combined speed was 75mph.

A bit of mental arithmetic will then find that, if the sum of their speeds is 75mph and one speed is 15mph faster than the other, then the two speeds are 30mph and 45mph.