Question

Kiran drove from Tortula to Cactus, a distance of 224 mi. She increased her speed by 9 mi/h for the 340 mi trip from Cactus to Dry Junction. If the total trip took 12 h, what was her speed from Tortula to Cactus?

Answer 1

Basic info you'll need: d=rt.
In words, "distance covered equals rate (speed), r, times time, t.

You can solve d=rt for either r or t if needed.

Represent Kiran's initial rate (speed) by s. She increases her speed by 9 mph for the second half of her trip. How would you represent this greater speed algebraiclally, if her initial speed was s?

Answer 2

Next question for you: How would you represent algebraically the time required to drive each leg of Kiran's trip? Most likely you'll have to represent two different times.

Answer 3

s+9

Answer 4

Not sure...

Answer 5

I know the total trip was 564 miles and it took 12 hours so her average speed was 47mph.

Answer 6

You could represent the first distance by d1 and the second by d2 (or by x and y).

Then d1 + d2 = 564 mi

How would you represent the 2 different speeds?

How would you represent the 2 different times?

Once you have those representations done, we can begin solving the problem for the speed at which Kiran drove from Tortula to Cactus.

Answer 7

The speeds would be represented by r and r+9.

Answer 8

The times would be t1 and t2, I think.

Answer 9

those representations are fine. Our job is to find r, and then r+9, which is the final result desired.

Suppose Kiran drives at rate 'r for t1 hours. How great a distance will he cover?
Suppose he drives at rate (r+9) for t2 hours. How great a dist. will he cover?

Answer 10

Now add these two symbolic distances together and equate the sum to the known total distance, 564 miles. What does your equation look like?

Answer 11

what is the total time consumed by the trip? Can you write an equation in time only that represents this? Use t1 and t2.

Answer 12

Experimenting with this situation, I've ended up with two equations in two unknowns, r and t2. Two equations in two unknowns can be solved simultaneously for r and t2.

Care to give that a try?

Answer 13

"Suppose Kiran drives at rate 'r for t1 hours. How great a distance will he cover?"

Recall: distance = (rate) * (time).
Here, that distance would be ( r ) * ( t1 ).

During the second part of Kiran's trip, he or she would cover ( r + 9 ) * ( t2 ) miles.

Please review this conversation and see what you can do with these representations.
We want to boil things down to the point where you have 2 equations in 2 unknowns.