A bus riddle
A bus was scheduled to travel from Town A to Town B at a constant speed of Qkm/h. If the speed of the bus was increased by 20%,it would arrive at Town B 2 hours ahead of schedule. However,if the bus travelled the first 240 km at Qkm/h and then the speed was decreased to 80%,it could arrive at Town B 2 hours behind schedule. Find the distance,in km,between the 2 towns.(neglect the units)
The answer is 720.
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1 solution
Qkm/h -on time (1.2)Qkm/h-2 hours early Town A-(first 240km at Qkm/h)-Town B-(0.8)Qkm/h-2 hours late SPEED-5 units(original speed) SPEED-6 units(new speed) TIME-6 units(original time) TIME-5 units(new time) This is correct if the speed of the bus increased by 20%. We see that 1 unit is 2 hours. The time if the original speed is taken to reach Town B is 12(6 times 2) hours. The time if the new speed is taken to reach Town B is 10(5 times 2)hours. Now,what if the bus travelled the first 240 km at Qkm/h and then decreased to 80%? SPEED-5 units(original speed unchanged) SPEED-4 units(new speed changed) TIME-4 units(original speed) TIME-5 units(new speed) 1 unit=2 hours 4 units=8 hours 240 divide 4 is 60(Qkm) 60 times 12 is 720. Hence,the distance between the 2 towns is 720 km.