# Thread: Word Problem - Car Travel

1. ## Word Problem - Car Travel

A car travels from one town to another at a speed of 32mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?

So far I have rate of 32mph, 32+4
x = initial time
y = x-1/2

2. Originally Posted by mcruz65
A car travels from one town to another at a speed of 32mph. If it had gone 4 mph faster, it could have made the trip in 1/2 hr less time. How far apart are the towns?

So far I have rate of 32mph, 32+4
x = initial time
y = x-1/2

speed= distance/time so, letting d be the distance between the two towns, in miles, and t be the time, in hours, for the trip, 32= d/t.

If "it had gone 4mph faster" its speed would have been 32+ 4= 36 and "it could have made the trip in 1/2 hr less time" so the time would be t- 1/2. Now "speed= distance/time" so 36= d/(t+1/2).

32= d/t is the same as d= 32t.
36= d/(t+1/2) is the same as d= 36(t+1/2)= 36t+ 18.

d= 32t= 36t+ 18.

Solve 32t= 36t+ 18 for t and then use d= 32t to find the distance between the towns.

3. ## Word Problem - Car Travel

Ok this is what I have so far.

32t = 36t + 18
-36t + 32t = 18
-4t = 18

-4t/-4 = 18/-4
t= -4.5

d=32t
d=32(-4.5)
d= -144 I don't understand why the answer is negative. Where did I go wrong?

4. Shouldn't it be 36 = d/(t-1/2), as it takes less time at a higher speed?
Which leaves you with an answer of t = 4.5

5. ## Word Problem - Car Travel

So you are saying that the equations should be like this.

36t = 32t + 18
36t - 32t = -32t + 18
4t = 18
4t/4 = 18/4
t = 4.5

d=32t
d=32(4.5)
d=144

Is this correct?

6. Hmm that looks overly confusing, mine was like:
$32 = \frac{d}{t}$
$d = 32t$

$36 = \frac{d}{t-\frac{1}{2}}$
$d = 36(t-\frac{1}{2}) = 36t - 18$

$\therefore 32t = 36t - 18$
$-4t = -18$
$t = \frac{-18}{-4} = 4\frac{1}{2}$

Then obviously sub into d=32t like you have done to get 144.

36t - 32t = -32t + 18
Does not simplify to 4t = 18, the -32t on each side would cancel to leave 36t = 18 so you've gone wrong somewhere.

7. Let t = time in minutes

(32mph)(t)= (36 mph)(t-30)

32t= 36t- 1080

-4t= -1080

t= 270 minutes

270 minutes

(32 miles/hour)/(60 min) = .533333 miles/min

(.533333 miles/min)(270 min) is about 144 miles