Two cars A and B 250 km apart are travelling towars each other on the same
road . The tavelling speed of car B is 5 km/h more than 5/7 of the speed of car A . they will meet after 2 hour . Find the travelling speed of each car .
英文 數學中一
2009-11-09 8:57 am
回答 (2)
2009-11-09 7:54 pm
Let Va be the speed of car A, and Vb be the speed of car B
Since the two cars are travelling in opposite direction towards one another, the speed of car A relative to car B = Va - (-Vb) = Va + Vb
Using distance = speed x time
250 = (Va + Vb).(2)
i.e. Vb = 250/2 - Va = 125 - Va
But Vb = (5Va/7) + 5
hence, 125 - Va = 5Va/7 + 5
12Va/7 = 120
Va = 120x7/12 km/h = 70 km/h
and Vb = (125-70) km/h = 55 km/h
Since the two cars are travelling in opposite direction towards one another, the speed of car A relative to car B = Va - (-Vb) = Va + Vb
Using distance = speed x time
250 = (Va + Vb).(2)
i.e. Vb = 250/2 - Va = 125 - Va
But Vb = (5Va/7) + 5
hence, 125 - Va = 5Va/7 + 5
12Va/7 = 120
Va = 120x7/12 km/h = 70 km/h
and Vb = (125-70) km/h = 55 km/h
2009-11-09 9:12 am
Let x km/h be the speed of car A
∴Speed of car B = (5x/7 + 5) km/h
∵They meet after 2 hours,
∴Distance travelled by car A = 2x km
Distance travelled by car B = 2(5x/7 + 5) km
2x - 2(5x/7 + 5) = 250
2x - 10x/7 - 10 = 250
4x/7 = 260
x = 455
∴The speed of car A = 455 km/h
The speed of car B = 5(455)/7 + 5 = 330 km/h
∴Speed of car B = (5x/7 + 5) km/h
∵They meet after 2 hours,
∴Distance travelled by car A = 2x km
Distance travelled by car B = 2(5x/7 + 5) km
2x - 2(5x/7 + 5) = 250
2x - 10x/7 - 10 = 250
4x/7 = 260
x = 455
∴The speed of car A = 455 km/h
The speed of car B = 5(455)/7 + 5 = 330 km/h
參考: me
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