Question

Mai, Clare, and Tyler are hiking

from a parking lot to the summit
of a mountain. They pass a sign
that gives distances.
Parking lot: 3/4 mile
Summit: 1 and 1/2 miles
Mai says: "We are one third of the
way there." Clare says: "We have to
go twice as far as we have already
gone." Tyler says: "The total hike is
three times as long as what we
have already gone."
Who is correct?

Answer 1

Mai, Clare, and Tyler are hiking from a parking lot to the summit of a mountain. Clare is correct in saying that they have to go twice as far as they have already gone.

Step-by-step explanation:

In order to determine who is correct, let's first find the fractions of the total distance that Mai, Clare, and Tyler have already traveled:

Mai has traveled 3/4 mile out of a total distance of 1 and 1/2 miles. To find the fraction, divide 3/4 by 1 and 1/2:

3/4 ÷ 1 and 1/2 = 3/4 ÷ 3/2 = 3/4 × 2/3 = 1/2

So Mai has traveled half of the total distance, not one third.

Clare has traveled 3/4 mile and says they have to go twice as far as they have already gone. If we double 3/4 mile:

3/4 mile × 2 = 6/4 mile = 1 and 1/2 miles

So Clare is correct. They have to go 1 and 1/2 miles, which is twice the distance they have already gone.

Tyler says the total hike is three times as long as what they have already gone. If we multiply 3/4 mile by 3:

3/4 mile × 3 = 9/4 mile = 2 and 1/4 miles

So Tyler is incorrect. The total hike is 1 and 1/2 miles, not 2 and 1/4 miles.

In conclusion, Clare is the only one who is correct.

Answer 2

Answer:Yes, they are all correct

Step-by-step explanation:

From the attached image, we see that the sign is showing;

Parking lot: ¾ miles

Summit: 1½ miles

Summit distance can also be expressed as an improper fraction = 3/2 miles

Now, since they started hiking from the park to the summit, it means that they had moved ¾ mile from the parking lot and had 3/2 miles left to get to the summit.

Thus, total distance from parking lot to summit = ¾ + 3/2 = 9/4 miles

Now, let's analyze each of their statements;

Mai said they are a third of their way there.

They had covered 3/4 mile and the total distance is 9/4 miles.

Thus, fraction of total distance covered is;

9/4 ÷ 3/4 = 1/3.

So, Mai is correct

Clare said they have to go twice as far as they had already gone.

They had covered 3/4 miles.

Therefore, twice this = 2 × 3/4 = 6/4 = 3/2 which is same as the sign distance left to the summit.

Thus, Clare is correct

Tyler said that the total hike is three times as long as what we have already gone.

They had gone 3/4 miles

3 times this = 3 × 3/4 = 9/4 miles.

This tallies with the total distance calculated earlier.

Thus, they are all correct