Mathematics: You and a friend start riding bikes toward each other from opposite ends of a 24-mile biking route. you ride 2 1/6 miles every 1/4 hour . your friend rides 7 1/3 miles per hour. a. after how many hours do you meet? b. when you meet, who has traveled farther? how much farther?

answer: step-by-step explanation: 1...

You and a friend start riding bikes toward each

Ответ:

ajbrock1004

26.03.2021

Mathematics

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 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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You and a friend start riding bikes toward each other from opposite ends of a 24-mile biking route. you
ride 2 1/6 miles every 1/4 hour . your friend rides 7 1/3 miles per hour.
a. after how many hours do you meet?
b. when you meet, who has traveled farther? how much farther?

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You and a friend start riding bikes toward each other from opposite ends of a 24-mile biking route. you ride 2 1/6 miles every 1/4 hour . your friend rides 7 1/3 miles per hour. a. after how many hours do you meet? b. when you meet, who has traveled farther? how much farther? ​

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You and a friend start riding bikes toward each other from opposite ends of a 24-mile biking route. you
ride 2 1/6 miles every 1/4 hour . your friend rides 7 1/3 miles per hour.
a. after how many hours do you meet?
b. when you meet, who has traveled farther? how much farther?