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Karo-lina-s [1.5K]
2 years ago
15

You and a friend start riding bikes toward

Mathematics
1 answer:
Setler [38]2 years ago
7 0

Answer:

1.5 hours

I traveled farther

2 miles

Step-by-step explanation:

\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}

My speed

\dfrac{2\dfrac{1}{6}}{\dfrac{1}{4}}=\dfrac{\dfrac{13}{6}}{\dfrac{1}{4}}=\dfrac{26}{3}\ \text{mph}

Speed of my friend

7\dfrac{1}{3}=\dfrac{22}{3}\ \text{mph}

Time passed for both me and my friend will be equal if we start at the same time and the combined distance covered by both of us will be 24 miles. Let t be the time taken to meet

\text{Distance}=\text{Speed}\times\text{Time}

\dfrac{26}{3}t+\dfrac{22}{3}t=24\\\Rightarrow \dfrac{48}{3}t=24\\\Rightarrow 16t=24\\\Rightarrow t=\dfrac{24}{16}\\\Rightarrow t=1.5\ \text{hours}

So, we meet each other after 1.5 hours.

Distance traveled by me

\dfrac{26}{3}\times 1.5=13\ \text{miles}

Distance traveled by my friend

\dfrac{22}{3}\times 1.5=11\ \text{miles}

So, I traveled farther by 13-11=2\ \text{miles}.

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serg [7]
<span>let x = the number of liters of the 20% solution. 

let y = the number of liters of the 60% solution. 

you want x + y to be equal to 40 liters. 

x is the number of liters total in the first solution.
y is the number of liters total in the second solution. 

you want .2 * x + .6 * y to be equal to .35 * 40 

.2 * x is the number of liters of acid in the first solution.
.6 * y is the number of liters of acid in the second solution.
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you have two equations that need to be solved simultaneously. 

they are: 

x + y = 40
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simplify these equations to get: 


x + y = 40
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you can solve by substitution or by elimination or by graphing.
i will solve this one by graphing.
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the graph looks like this: 

 
the graph says the intersection is at the coordinate point of (25,15). 

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x is the number of liters of the 20% solution.
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the formula of .2x + .6y = 14 becomes .2 * 25 + .6 * 15 = 14.
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