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When Mr. Peters drives from Boston to Worcester it takes him 30 minutes travelling at a speed of 60 miles per hour. Mrs. Peters drives from Boston to Worcester and leaves 5 minutes after Mr. Peters but travels at a speed of 90 miles per hour. Who will arrive first? By how many minutes?

Respuesta :

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Since the problem is requesting the answer in minutes, we are going to convert the speed of Mr. Peter to miles per minutes; to do that, we are going to multiply his speed by the multiplier [tex] \frac{60min}{1h} [/tex]:
[tex]60 \frac{miles}{h} * \frac{1h}{60min} =1 \frac{mile}{min} [/tex]

Now, to find the distance from Boston to Worcester, we are going to use the distance formula: [tex]d=vt[/tex]
where
[tex]d[/tex] is the distance
[tex]v[/tex] is the speed
[tex]t[/tex] is the time 

We know that the speed of Mr. Peter is [tex]1 \frac{mile}{min}[/tex] and his time is 30 minutes. Lets replace those values in our formula:
[tex]d=1 \frac{mile}{min} *30min[/tex]
[tex]d=30miles[/tex]

Now, lets concentrate on Mr. Peter clone, Mr. P:
Lets convert the speed of Mr. P to miles per minute:
[tex] \frac{90miles}{h} * \frac{1h}{60min} =1.5 \frac{miles}{min} [/tex]
We also know that they will cover the same distance, 30 miles. Lets replace the values in our formula one more time to find t:
[tex]d=vt[/tex]
[tex]30miles= 1.5\frac{miles}{min} *t[/tex]
[tex]t= \frac{30miles}{1.5\frac{miles}{min}} [/tex]
[tex]t=20min[/tex]
But since Mr. P leaves 5 minutes after Mr. Peters, we need to add those 5 minutes to M. P's time:
[tex]t=20min+5min[/tex]
[tex]t=25min[/tex]

We can conclude that Mr. P will arrive first, 5 minutes before Mr. Peter.

Mrs. Peter arrives 5 minutes before Mr. Peter

To find who arrives first we first need to find the speed and time they require to arrive.

Given : From Boston to Worcester

            Mr. Peter takes [tex]\rm time=30 \; minutes \; and \;speed= 60 miles /hr[/tex]

            Mrs. Peter takes [tex]\rm speed=90 miles/hr[/tex]

We will now calculate Mr. Peters speed,

[tex]\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}[/tex]

How to find distance from Boston to Worecester?

To find the distance, we will use distance formula

[tex]\rm Distance=speed\times time[/tex]

Here,given that the Mr Peters speed is [tex]\rm 60 miles /hr[/tex] and time is [tex]\rm 30 minutes[/tex]so by distance formula we will find distance of Mr. Peter

[tex]\rm Distance=\dfrac{mile}{min} \times 30 minutes[/tex]

[tex]\rm Distance= 30 miles[/tex]

Similarly, we will now calculate Mrs. Peters speed,

[tex]\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}[/tex]

by the given informations we know both covers the same distance

[tex]\rm ie. \;30 miles[/tex]

we will now find distance of Mrs. Peter

[tex]\rm Distance=speed\times time\\ 30miles=1.5\dfrac{miles}{min} \times time\\ time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\ time=20 minutes[/tex]

Here, we know that Mrs.Peter leaves from Boston to Worcester 5 minutes after Mr.Peter so we will add 5 minutes to Mrs. Peters time.

[tex]\rm time=20 minutes+ 5 minutes\\ time=25 minutes[/tex]

Therefore, it is clear that Mrs.Peter arrive before Mr Peter by 5minutes.

Learn more about Distance formula here: https://brainly.com/question/9954116

           

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