SOLUTION: Betty and Carl live in the same apartment building, work at the same office, and set off for work in the morning at the same time. They must each travel 65 km, and they arrive at w

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Question 1127557: Betty and Carl live in the same apartment building, work at the same office, and set off for work in the morning at the same time. They must each travel 65 km, and they arrive at work at the same time. Betty travels by car at 45 km/h, parks the car and then walks at 5 km/h the rest of the way to work. Carl takes the bus, which travels at 40 km/h, to the same car park as Betty uses, and then rides his bike the rest of the way at 6 km/h. If they both leave leave at 6 a.m, at what time do they arrive to work?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Let x be the distance from the car park to work; then 65-x is the distance from the apartment building to the car park.

Betty travels the 65-x miles at 45mph and the x miles at 5mph. Carl travels the 65-x miles at 40mph and the x miles at 6mph. The time they take is the same. So









The total time in hours for Betty is



The total time for Carl is



It takes each of then 7/3 hours, or 2 1/3 hours, to get to work. Since they leave at 6:00am, they arrive at 8:20am.
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Let x be the distance from the apartment building to the parking.


Then we have the time equation


    Betty's total travel time  =  Carl's total travel rime


                      =  


Multiply both sides by 45*5*40*6


    5*40*6x + 45*40*6*(65-x) = 45*5*6*x + 45*5*40*(65-x)

    5*40*6x - 45*40*6x - 45*5*6x + 45*5*40x = 45*5*40*65 - 45*40*6*65

    (5*40*6 - 45*40*6 - 45*5*6 + 45*5*40)x = 45*5*40*65 - 45*40*6*65

    -1950x = -117000

    x = {{(-117000)/(-1950)}}} = 60.


Thus we found the distance x = 60 miles.


Hence, Betty spends   +  hours = 1 hour 20 minutes + 1 hour = 2 hours and 20 minutes.


To check, Carl spends the same time   +  hours = 1 hour 30 minutes + 50 minutes = 2 hours and 20 minutes.


Hence, they both arrive to work at 8:20 am.


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