Question 1208786: 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 at the car park, 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 home at 6 a.m., at what time do they arrive at work?
Answer by ikleyn(52817)   (Show Source):
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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 at the car park, 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 home at 6 a.m., at what time do they arrive at work?
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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.
Solved.
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