Mathematics, 21.07.2019 16:30 cookiee1387

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?

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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 $\frac{60min}{1h}$ :
$60 \frac{miles}{h} * \frac{1h}{60min} =1 \frac{mile}{min}$

Now, to find the distance from Boston to Worcester, we are going to use the distance formula: d=vt

where

is the distance

is the speed

is the time

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

Now, lets concentrate on Mr. Peter clone, Mr. P:
Lets convert the speed of Mr. P to miles per minute:
$\frac{90miles}{h} * \frac{1h}{60min} =1.5 \frac{miles}{min}$
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:
d=vt

$30miles= 1.5\frac{miles}{min} *t$
$t= \frac{30miles}{1.5\frac{miles}{min}}$
t=20min

But since Mr. P leaves 5 minutes after Mr. Peters, we need to add those 5 minutes to M. P's time:
t=20min+5min

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

Answer from: cortneykeeler

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 $\rm time=30 \; minutes \; and \;speed= 60 miles /hr$

Mrs. Peter takes $\rm speed=90 miles/hr$

We will now calculate Mr. Peters speed,

$\rm 60 \dfrac{miles}{h} \times \dfrac{h}{60minutes}=\dfrac{mile}{min}$

How to find distance from Boston to Worecester?

To find the distance, we will use distance formula

$\rm Distance=speed\times time$

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

$\rm Distance=\dfrac{mile}{min} \times 30 minutes$

$\rm Distance= 30 miles$

Similarly, we will now calculate Mrs. Peters speed,

$\rm \dfrac{90miles}{h} \times \dfrac{h}{60minutes}=1.5\times \dfrac{miles}{min}$

by the given informations we know both covers the same distance

$\rm ie. \;30 miles$

we will now find distance of Mrs. Peter

$\rm Distance=speed\times time\\
30miles=1.5\dfrac{miles}{min} \times time\\
time=\dfrac{30miles}{1.5\dfrac{miles}{min}}\\\\
time=20 minutes$

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.

$\rm time=20 minutes+ 5 minutes\\
time=25 minutes$

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

Learn more about Distance formula here: link

Answer from: Quest

Ireally wish i can my h

Answer from: Quest

step-by-step explanation:

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