SOLUTION: 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 65 km, and they arrive at w

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: 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 65 km, and they arrive at w      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1127557: 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 65 km, and they arrive at work at the same time. Betty travels by car at 45 km/h, parks the car and then walks at 5 km/h the rest of the way to work. Carl takes the bus, which travels at 40 km/h, to the same car park as Betty uses, and then rides his bike the rest of the way at 6 km/h. If they both leave leave at 6 a.m, at what time do they arrive to work?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the distance from the car park to work; then 65-x is the distance from the apartment building to the car park.

Betty travels the 65-x miles at 45mph and the x miles at 5mph. Carl travels the 65-x miles at 40mph and the x miles at 6mph. The time they take is the same. So

%2865-x%29%2F45%2Bx%2F5+=+%2865-x%29%2F40%2Bx%2F6
%2865-x%29%2F45%2B9x%2F45+=+%28195-3x%29%2F120%2B20x%2F120
%288x%2B65%29%2F45+=+%2817x%2B195%29%2F120
120%288x%2B65%29+=+45%2817x%2B195%29
960x%2B7800+=+765x%2B8775
195x+=+975
x+=+5

The total time in hours for Betty is

60%2F45%2B5%2F5+=+4%2F3%2B1+=+7%2F3

The total time for Carl is

60%2F40%2B5%2F6+=+3%2F2%2B5%2F6+=+9%2F6%2B5%2F6+=+14%2F6+=+7%2F3

It takes each of then 7/3 hours, or 2 1/3 hours, to get to work. Since they leave at 6:00am, they arrive at 8:20am.

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the distance from the apartment building to the parking.


Then we have the time equation


    Betty's total travel time  =  Carl's total travel rime


    x%2F45+%2B+%2865-x%29%2F5                  =  x%2F40+%2B+%2865-x%29%2F6


Multiply both sides by 45*5*40*6


    5*40*6x + 45*40*6*(65-x) = 45*5*6*x + 45*5*40*(65-x)

    5*40*6x - 45*40*6x - 45*5*6x + 45*5*40x = 45*5*40*65 - 45*40*6*65

    (5*40*6 - 45*40*6 - 45*5*6 + 45*5*40)x = 45*5*40*65 - 45*40*6*65

    -1950x = -117000

    x = {{(-117000)/(-1950)}}} = 60.


Thus we found the distance x = 60 miles.


Hence, Betty spends  60%2F45 + 5%2F5 hours = 1 hour 20 minutes + 1 hour = 2 hours and 20 minutes.


To check, Carl spends the same time  60%2F40 + 5%2F6 hours = 1 hour 30 minutes + 50 minutes = 2 hours and 20 minutes.


Hence, they both arrive to work at 8:20 am.