word problem help please?

Question

Ariana took 2 h longer to drive 360 mi. on the first day of a trip than she took 270 mi. on the second day. If her speed was the same on both days, what was the driving time each day?

Answer 1

Ok, call r the rate of travel (speed and t the time on the shorter day.

You can say that:

r * t = 270, and for the second day, the time was 2 hours longer, and the distance was 360 so:

r * (t+2) = 360

Solve for r in the first one: r = 270/t, and sub that into the second

(270/t) * (t+2) = 360

That simplifies to 270 + (540/t) = 360
540/t = 90

t = 6, so t+2 = 8

The shorter day was 6 hours and the longer one was 8. If you need to know her speed, it would be 270/6 = 45 mph :)

Answer 2

This is a Distance:Rate:Time problem. In all cases
where one of these three variables is involved, the
formula that connects them is Distance=Rate X Time

This problem tells us the following information:
Dist. Rate Time Day
360 . R(1)..x+2....1
270...R(2)....x......2

We are told that her speed was the same both days.
Day (1) speed = D/T, or 360/(x+2)
Day (2) speed = D/T, 0r 270/x
Thus, 360/(x+2)=270/x
Cross-multiplying gives me 360x=270(x+2)
360x=270x+540
360x-270x=540
90x=540
x=6
Day 1 was x+2, so day 1=8 hours
Day 2 = 6 hours.

In problems like these, you have to be comfortable
with manipulating D=R X T
If it's T you're after, solve the D=RT formula for T by
dividing both sides by R, to get T =D/R
Similarly, R=D/T.

Answer 3

6 hrs. each day
360-270 ml = 90 ml for 2 hr.
270/90 = 3 hrs x 2 = 6 hrs.