Shirley traveled 6 hours to Lake Sinclair, a total of 315 miles. She took a train part way of the way, which averaged 50 miles per hour and then took the bus th

Question

Shirley traveled 6 hours to Lake Sinclair, a total of 315 miles. She took a train part way of the way, which averaged 50 miles per hour and then took the bus the remaining distance, which averaged 65 miles per hour. How long was Shirley on the train?

Answer 1

Let x = distance traveled by train.  Then 315 - x = distance traveled by bus.

 

Distance = (Rate)(Time), so Time = distance/rate

 

(Time on the train) + (Time on the bus) = 6

 

So, x/50 + (315-x)/65 = 6

 

Multiply the equation by the LCD, 650:  13x + 10(315-x) = 3900

 

                                                           3x + 3150 = 3900

 

                                                                      3x = 750

 

                                                                        x = 250 miles

 

Time on the train = x/50 = (250 miles)/(50 miles/hour) = 5 hours

Answer 2

t is time on train

b is time on bus

 

t + b = 6, or t = 6 - b

 

50t is distance on train

65b is distance on bus

 

50t + 65b = 315              substitute t from above

50(6 - b) + 65b = 315

300 - 50b + 65b = 315

300 + 15b = 315

15b = 15

b = 1

 

She was on the train fro 5 hours.

 

Check

 

5(50) + 1(65)

250 + 65

315