Algebra Word Problem?

Question

Leon drove 270 miles to the lodge in the same time Pat drove 330 to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?

Answer 1

270/x = 330/(x+10)

or 9/x = 11/(x+10)

or 9x + 90 = 11x

or x =45

and Pat drove at 55 miles / hr.

Answer 2

Distance = speed x time. Rearranging we see that
Time = Distance / speed

The problems says that the times that each drove was the same. So, let's say that Leon's speed is x. Pat's is x + 10. So, Leon's time = 270/x while Pat's is 330/(x+10). Since the times are the same we have

270/x = 330/(x+10) Now, multiply both side by x

270 = (330x)/(x+10) Now multiply both sides by (x+10)

270(x + 10) = 330x
270x + 2700 = 330x
2700 = 330x - 270x
2700 = 60x
2700/60 = x
x = 45 mph

HTH

Charles

Answer 3

t = time
v = velocity of leon

now velocity * time = distance
270 = t * v
330 = t * (v + 10)

Now because we have no idea how much time they spent driving you have to substitute it out of the equation
In other words
270 = t * v
t = 270 / v

substitute into the other equation :
330 = t * (v + 10)
330 = (270 / v) * ( v + 10)
330 = 270 + 2700 / v
60 = 2700 / v
60 v = 2700
v = 45 mi / h

Leon drove 45 mi / h

Pat drove 55 mi / h

Answer 4

Leon
T = 270/s..........T=d/s


Pat
T= 330/(s+10)

270/s = 330/(s+10)
=> 270(s+10) = 330s
the rest is easy