SAT数学备考经典模拟题训练27

>>SAT数学模拟题：SAT数学备考经典模拟题训练27

>>SAT考试辅导

· Question #4: A vehicle runs from town A to town B at a speed of 20 miles/hour while another vehicle runs from town B to town A at a speed of 60 miles/hour. Both vehicles start their trips at the same time and the distance between towns is 100 miles. How long does it take from the time they start running to the moment they are at the same point on the road?

(a) 1 hour

(b) 1 hour and 15 minutes

(c) 1 hour and 30 minutes

(d) 1 hour and 45 minutes

(e) 2 hours and 15 minutes

解析

o Answer: If angle AMB is 100o, then angle BME is 180o - 100o = 80o

BMC + CMD = 40o

BMC + CMD + DME = 80o

If we subtract the 2 equations, DME = 40o

CMD + DME = 60o

BMC + CMD + DME = 80o

If we subtract the 2 equations, BMC = 20o

CMD = BME - BMC - DME = 80o - 40o - 20o = 20o

o 100 miles = d1 + d2 This is equation #1.

It take the same time for the 2 cars to meet: t = d1/(20 miles/hour) = d2/(60miles/hour). This is equation #2.

We solve the system of 2 equations to find d1 and d2.

From equation #2, 3·d1 = d2.

Then 100 miles = d1 + d2 = 4·d1, so d1 = 25 miles and d2 = 75 miles.

The answer is t = d1/20miles/hour = 25/20 = 5/4 = 1 hour and 15 minutes.

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