Question 1204580: 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 40 km, and they arrive at work at the same time. Betty travels by car at 40 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 20 km/h, to the same car park as Betty uses, and then rides his bike the rest of the way at 8 km/h. If they both leave home at 6 a.m., at what time do they arrive at work?
Answer by mananth(16946)   (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 40 km, and they arrive at work at the same time. Betty travels by car at 40 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 20 km/h, to the same car park as Betty uses, and then rides his bike the rest of the way at 8 km/h. If they both leave home at 6 a.m., at what time do they arrive at work?
Let x be the distance from home to car park
car park to office distance will be (40-x)
Time taken by Betty = Time by car + walking time from car park =x/40 + (40-x)/5
Time taken by Carl = Time by bus + cycling time from car park = x/20+(40-x)/8
For both of them time taken is same. Equate both
x/40 + (40-x)/5 = x/20+(40-x)/8
x+8(40-x)= 2x+5(40-x)
x+320-8x= 2x+200-5x
120=4x
x= 30 Distance to car park
car park to office 10 km
Time taken by betty
30/40 + 10/5 = 2.75 hours
Time taken by Carl
30/20 +10/8= 2.75 hours
You calculate what time they reach.
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