SOLUTION: AN ACCOUNTANT RIDES THE BUS PART OF THE WAYTO WORK EVERY DAY AND WALKS THE REST. THE BUS RIDES 40 MPH AND THE ACCOUNTANT WALK 3MPH. THE DISTANCE FROM WORK IS 23 MILES. THE TOTAL TI

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Question 117628: AN ACCOUNTANT RIDES THE BUS PART OF THE WAYTO WORK EVERY DAY AND WALKS THE REST. THE BUS RIDES 40 MPH AND THE ACCOUNTANT WALK 3MPH. THE DISTANCE FROM WORK IS 23 MILES. THE TOTAL TIME IT TAKES THE ACCOUNTANT TO GO TO WORK IS 3HRS. HOW FAR DOES THE ACCOUNTANT WALKS?
Found 2 solutions by Fombitz, checkley71:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate x Time = Distance
Distance = Rate/Time
Let's call Bus Time and Bus Distance, T1 and D1.
Let's call walk time and walk distance, T2 and D2.
1.D1%2BD2=23 Total distance is 23 miles.
2.T1%2BT2=3 Total time is 3 hours.
3.D1%2FT1=40 Rate of the bus is 40 mph.
4.D2%2FT2=3 Rate of the accountant walking is 3 mph.
From 3,
3.D1%2FT1=40
D1=40T1
and from 4,
4.D2%2FT2=3
D2=3T2
You can substitute these values into 1.
1.D1%2BD2=23
40T1%2B3T2=23
3T2=23-40T1
T2=%2823-40T1%29%2F3
You can substitute this value for T2 into equation 2 and solve for T1.
2.T1%2BT2=3
T1%2B%2823-40T1%29%2F3=3
3T1%2B23-40T1=9
23-37T1=9
-37T1=-14
T1=14%2F37
From 2,
T1%2BT2=3
14%2F37%2BT2=3
T2=3-14%2F37
T2=111%2F37-14%2F37
T2=97%2F37
From 3,
D1=40T1
D1=40%2814%2F37%29
D1=560%2F37
From 4,
D2=3T2
D2=3%2897%2F37%29
D2=291%2F37
So in approximate terms, the accountant rides the bus 15.1 miles for 0.38 hrs(22 minutes) and then walks 2.62 hrs (2 hrs, 38 minutes) for a distance of 7.9 miles.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
40X+3(3-X)=23
40X+9-3X=23
37X=23-9
37X=14
X=14/37
X=.3784 HOURS FOR THE TIME OF THE BUS RIDE.
3-.3784=2.6216 HOURS FOR THE WALKING TIME.
PROOF:
.3784*40+3(2.6216)=23
15.136+7.864=23
23=23