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timurjin [86]
3 years ago
15

Sal was tired of waiting for Amir to show up at their meeting place, so he started running at an average speed of 4.5 mph withou

t him. Ten minutes later, Amir still had 0.25 of a mile to go before he reached the meeting place, but Sal was 0.75 of a mile beyond it. If Amir is running at a faster pace, 6.7 mph, to the nearest hundredth of an hour, after how much time will Amir catch up to Sal?
Mathematics
2 answers:
kvasek [131]3 years ago
5 0

Answer:

Hence, after 0.45 hour Amir will catch up to Sal.

Step-by-step explanation:

Let A(t) and S(t) denote the function that represent the  distance of that Sal and Amir covers over a period of time 't'.

We have to find the value of t such that:

S(t)=A(t)

As it is given that:

Amir is running at a faster pace, 6.7 mph, Amir still had 0.25 of a mile to go before he reached the meeting place.

so,

A(t)= -0.25+6.7t

Also,

Sal is running at an average speed of 4.5 mph, but Sal was 0.75 of a mile beyond it.

This means that:

S(t)=0.75+4.5t

Also now,

A(t)=S(t)

⇒  -0.25+6.7t=0.75+4.5t

⇒ 6.7t-4.5t=0.75+0.25

⇒ 2.2t=1

⇒ t=1/2.2

⇒ t=5/11

⇒ t≈0.45 hr.

Hence, after 0.45 hour Amir will catch up to Sal.

sergiy2304 [10]3 years ago
4 0
A=-.25+6.7t, s=.75+4.5t  when Amir catches up a=s so:

-.25+6.7t=.75+4.5t  add .25 to both sides

6.7t=1+4.5t subtract 4.5t from both sides

2.2t=1  divide both sides by 2.2

t=10/22 hr

t≈0.45 hr (to nearest hundredth)
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