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URGENT ALGEBRA!!!

to arrive at his appointment on time mr jones had to drive all the way from his home with the average speed of 60 mph. due to heavy traffic, he was 15 mph slower than he planned and arrived to the appointment 20 minutes later. how many miles from mr. jones' home was his appointment

Respuesta :

xEngineerOrg
Let's look at the problem for both scenarios.

Scenario 1. Mr. Jones drives at v1 = 60 mph, for time t1 = ? and distance d1 = ?

In this scenario we know with what speed Mr. Jones drove but we don't know how long it took and what was the distance.

Scenario 2. Mr. Jones drove 15 mph slower and arrives 20 minutes later.

This means that:
v2 = v1 - 15 = 60 - 15 = 45
t2 = t1 + 20
d2 = ?

What we know for sure is that the distance is the same for both scenarios:
d2 = d1

We also know that Speed = Distance / Time, which means that:
Distance = Speed x Time

Now we can write our equations:
d2 = v2 x t2 = (v1-15) x (t1+20)
d1 = v1 x t1

d1=d2 which means:
v1 x t1 = (v1-15) x (t1+20)

We replace the v1 value in the equation above and we write 20 minutes as 1/3 hours:
60 x t1 = (60 - 15) x (t1 + 1/3)
60 x t1 = 45 x (t1 + 1/3)
60 x t1 - 45 x t1 = 45/3
15 x t1 = 15

Solving this for t1, we get t1 = 1 hour. This means that the distance is:

d1 = 60 x 1 = 60 miles

aksnkj

60 miles from Mr. jones' home was his appointment.

Given information:

To arrive at his appointment on time Mr. Jones had to drive all the way from his home with an average speed of 60 mph.

Due to heavy traffic, he was 15 mph slower than he planned and arrived at the appointment 20 minutes or 0.33 hours later.

The actual average speed of Mr. Jones is 60-15=45 mph.

Let d be the distance in miles between the office and the home and t be the time in hours required with speed 60 mph to reach the office.

The relation between d and t can be written as,

[tex]60=\dfrac{d}{t}\\45=\dfrac{d}{t+0.33}[/tex]

Solve the above equations for time t as,

[tex]60=\dfrac{d}{t}\\60t=d\\45=\dfrac{d}{t+0.33}\\45(t+0.33)=d\\60t=45t+15\\t=1\rm\; hour[/tex]

So, the distance between the office and home can be calculated as,

[tex]d=st\\d=60\times 1\\d=60\rm\; miles[/tex]

Therefore, 60 miles from Mr. jones' home was his appointment.

For more details, refer to the link:

https://brainly.com/question/12577966

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