Problem Solving

Two long time friends want to meet for lunch on a free weekend. One friend Ann, lives in Portland, and the other, Bill, lives in Seattle. They decide to meet somewhere on the 200-mile stretch connecting the two cities, and they start driving simultaneously from their respective cities toward each other along the same route. Ann drives an average of 50 miles per hour, and Bill drives an average of 70 miles per hour. Approximately how many miles from Portland will the two meet?

a) 56.7
b) 60.0
c) 72.5
d) 83.3
e) 96.7

The OA is D.

Please, can any expert assist me with above problem? I don't have it clear. Thanks.

Two long time friends want to meet for lunch on a free weekend. One friend Ann, lives in Portland, and the other, Bill, lives in Seattle. They decide to meet somewhere on the 200-mile stretch connecting the two cities, and they start driving simultaneously from their respective cities toward each other along the same route. Ann drives an average of 50 miles per hour, and Bill drives an average of 70 miles per hour. Approximately how many miles from Portland will the two meet?

a) 56.7
b) 60.0
c) 72.5
d) 83.3
e) 96.7

The OA is D.

Please, can any expert assist me with above problem? I don't have it clear. Thanks.

Hi LUANDATO,
Let's take a look at your question.

The two cities Portland and seattle are 200 miles apart.
Let Anne covered a distance of x miles and Bill covered a distance of 200 - x miles when they met at point C.
The whole situation is represented in the image below.





Using the formula, Distance = Speed * Time, we can write two equations for Anne and Bill.
Anne covered a distance of x miles at a speed of 50 miles/hr in 't' hours, therefore,
$$x=50t---(i)$$

Bill covered a distance of(200 - x) miles at a speed of 70 miles/hr in 't' hours, therefore,
$$200-x=70t---(ii)$$

Plugin the value of x from Eq(i) in Eq(ii),
$$200-50t=70t$$
$$200=70t+50t$$
$$200=120t$$

$$t=\frac{200}{120}$$
$$t\approx1.6667$$

It means that Anne and Bill meet each other after 1.67 hours.

We are asked to find approximately how many miles from Portland will the two meet?
We can see in the image that Anne and Bill met each other x miles from portland. It means we need to find the value of x.
We can easily find x by plugging in the value of t in Eq(i),
$$x=50t$$
$$x=50(1.6667)$$
$$x\approx83.335$$

It means they met 83.3 miles from Portland.
Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

LUANDATO wrote:Two long time friends want to meet for lunch on a free weekend. One friend Ann, lives in Portland, and the other, Bill, lives in Seattle. They decide to meet somewhere on the 200-mile stretch connecting the two cities, and they start driving simultaneously from their respective cities toward each other along the same route. Ann drives an average of 50 miles per hour, and Bill drives an average of 70 miles per hour. Approximately how many miles from Portland will the two meet?

a) 56.7
b) 60.0
c) 72.5
d) 83.3
e) 96.7

Since Ann and Bill drive toward each other, they WORK TOGETHER to cover the 200 miles between them.
When people work together, ADD THEIR RATES.
The combined rate for Ann and Bill = 50+70 = 120 miles per hour.
Of every 120 miles traveled by Ann and Bill working together, 50 miles are traveled by Ann.
Implication:
From Portland, Ann will travel 50/120 of the 200-mile distance:
(50/120) * 200 = (5/12)(200) = (5/3)(50) = 250/3 ≈ 83.3 miles.

The correct answer is D.