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emmainna [20.7K]
3 years ago
15

Two cyclists start at the same point and travel in opposite directions. One cyclist travels

Mathematics
1 answer:
Shtirlitz [24]3 years ago
3 0
Distance = rate times time.

Let the first cyclist's rate be r1 and the 2nd cyclist's rate be r2.

Let r2 = r1 + 10   (km per hour).

The total distance between them after 3 hours is 174 km; using the distance= rate times time formula, we also get:

r1(3 hrs) + r2(3 hrs) = 174 km
Then
r1(3 hrs) + (r1+10)(3hrs) = 174 km

Then 3r1 + 3r1 + 30 = 174 

6r1 = 144, and r1 = 24 km/hr.  Then r2 = (24 + 10) km/hr = 34 km/hr.


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2 A garden hose supplies 36 gallons of water in 3 minutes. Use a table or eq
Vilka [71]

Answer  ↣ 12 gallons per minute

Step-by-step explanation ↣ Ok I'm gonna use ratios because I can't draw a graph here.

Ok so if the garden hose supplies 36 gallons of water in 3 minutes, then the ratio is 36:3 because every 3 minutes the garden hose "sprays" 36 gallons.

To simplify this ratio, you need find the amount of water the garden hose supplies in 1 minute.

Well to get from 3 to 1, you have to divide by 3.

Do the same thing to 36. 36/3 equals 12.

So the final ratio is 12:1

This is the unit rate. The unit rate is when one variable is 1 unit (most of the time it is speed).

You can multiply 1 by any number and multiply 12 by the same number.

Here are some ratios...

m=minutes

g=gallons

1m:12g

2m:24g

3m:36g

4m:48g

5m:60g

Hope this helped!

BTW why do I sound like this I'm not a aesthetic person-

8 0
3 years ago
Solve each system using elimination. 3x+3y=27 x-3y=-11
Natalija [7]

Answer:

x=4

y=10

Step-by-step explanation:

3x +3y = 27

x - 3y = -11 (add these up so 3y will be eliminated and you'll have x only)

4x = 16

now let's eliminate x (you can put 4 instead of x though)

3x + 3y = 27

-3/ x -3y= -11 (multiple the the 2nd equation with -3 to eliminate x )

3x + 3y =27

-3x + 3y =33

6y = 60

8 0
4 years ago
I need to figure out what x is for my homework and I’m so confused teehee.
garik1379 [7]

Answer:

x = 9

Step-by-step explanation:

set a proportion: 8/12 = 6/x => 8x = 72 => x = 9

3 0
3 years ago
Explain how to solve 5^(x − 2) = 8 using the change of base formula log base b of y equals log y over log b.
Ray Of Light [21]

Answer:

x = 3.3

Step-by-step explanation:

A equation is given to us and we need to solve out for x. The given equation is ,

Take log on both sides with base as " 10" . We have ,

Simplify using the property of log ,  , we have ,

Simplify ,

Again simplify using the property of log ,

We know that log 5 = 0.69 and log 2 = 0.301 , on substituting this , we have ,

Simplify the RHS ,

Add 2 both sides ,

Hence the Value of x is 3.30 .

3 0
2 years ago
college students are offered a 8% discount on a textbook that sells for $31.50 if the sales tax is 8% , find the cost of the tex
zhenek [66]
The answer should be $33.99
8 0
3 years ago
Read 2 more answers
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