Anyone know algebra well?

Question

Terry and Reyanne went out for a bike ride into the country. They averaged 24 miles per hour on the way out and 18 miles per hour on the way back, by the same roads. Their total travel time was 7 hours. How far did they go?

Answer 1

Let x be the distance to destination

a is the time to go to

b is the time to return

a + b = 7

x=24a ....or

x=18b

therefore 24a=18b

or

a=18b/24

a=3b/4

but

a + b = 7

3b/4 + b = 7

7b/4=7

b=4

x = 18b

x = 18(4)

x = 72 mi.

How far did they go?

The question is how far is their destination, so 72mi.

Answer 2

First of all, think of the relationship between how fast one travels and how far one gets over time. Suppose I travel 24 miles per hour (mph), after 1 hour I would have gotten 1 hour x 24 mph = 24 miles. After 2 hours, I would have gone 2 hours x 24 mph = 48 miles. After 3 hours, it'd be 3 h x 24 mph = 72 miles.

1 h x 24 mph == 24 miles
2 h x 24 mph == 48 miles
3 h x 24 mph == 72 miles
4 h x 24 mph == 96 miles
5 h x 24 mph == 120 miles

See the relationship yet? Time x Rate == Distance.

Now, suppose Terry and Reyanne went from their home to a lake, then they came home. The distance travelled on the way there is the same distance on the way back.

Putting it all together, Time x Rate = Distance

Time going x Rate going = Distance going
Time returning x Rate returning = Distance returning

Distance going = Distance returning which means
Time going x Rate going = Time returning x Rate returning

Tg x Rg = Tr x Rr

Time going + Time returning = 7 hours (Tg + Tr = 7)

Rg = 24 mph Rr = 18 mph

Substitue values for the variables and you get

Tg x 24 mph = Tr x 18 mph
Tg x 24 mph = (7 - Tg) x 18 mph

Multiply then move the numbers around to solve for Tg and you get the time it took to get there. Now put it all back into the original relationship equation

Time going x Rate going = Distance going = Distance between home and lake
Tg (you just solved for this) x 24 mph = Distance, one-way.

Your question says "how far did they go?" which can be interpreted differently. Be sure to answer that the one-way distance is (the number you just solved), and that the total distance travelled is Distance going + Distance returning or twice the one-way distance.

Algebra is fun!

Answer 3

Let a = hours out
Let b = hours back

a + b = 7

s = vt

Since the distance both ways is the same,

v1 t1 = v2 t2

24 a = 18 b
a = 18 / 24 b = 3/4 b

a + b = 7

(3/4 b) + b = 7
7/4 b = 7
b = (4/7) 7 = 4

a + 4 = 7

a = 3
b = 4

3 (24) + 4 (18) = 144 mi

Answer 4

144 miles I think

It is. I just double checked myself with a diagram. 3 X 24 is 72, and 4 X 18 is 72. They went 72 miles one way, and turned around. Thats 144 total miles.

Answer 5

let t be the time they start, the total time is 7hrs, that means 7-t the time they return.

24t = 18(7-t)
24t = 126 - 18t
42t = 126
t = 3hr

x = vt
x = 24(3)
x = 72miles