SOLUTION: Jim traveled 240 miles to a convention. Later, his wife Ann drove up to meet him. Ann's average speed exceeded Jim's by 4 mph, and the trip took her 15 minutes less time. Find Ann'
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Question 606313: Jim traveled 240 miles to a convention. Later, his wife Ann drove up to meet him. Ann's average speed exceeded Jim's by 4 mph, and the trip took her 15 minutes less time. Find Ann's speed. Answer by vksarvepalli(154) (Show Source):
You can put this solution on YOUR website! Let the average speed of Jim be 'x' mph
so the average speed of Ann will be 'x+4' mph
let time taken by Jim to travel is 't' hrs.
then the time taken by Ann will be 't-0.25' hrs. (Since 15 mins = .25 hrs)
Now, average speed = total distance travelled / total time taken.
so, x = 240/t --- eq.1
x+4 = 240/(t-0.25) -----eq.2
Substituting eq.1 in eq.2
we get (240/t) + 4 = 240/(t-0.25)
=> 1/t + 1/60 = 1/(t-0.25)
=> 1/(t-0.25) - 1/t = 1/60
=> 4t^2-t-60 = 0
So t= 4 or t= -15/4
since time cannot be a negative value.
t = 4 hrs.
from eq.1 x = 240/t = 240/4 = 60 mph
So, Ann's speed = x+4 = 60+4 = 64 mph
Ans: 64 mph
