Question

Use the guess and check method to solve this problem.

Ranjit is journeying by foot and on horseback to a remote place.
She can travel 3 miles in an hour on foot or 7 miles in an hour on
horseback. After 10 hours, she has traveled 46 miles. How many
hours has she traveled on foot and on horse?
OA. 8 hours on foot and 2 hours on horse
B. 7 hours on foot and 3 hours on horse
OC. 5 hours on foot and 5 hours on horse
OD. 6 hours on foot and 4 hours on horse

Answer 1

To solve this problem, use the guess and check method to find the number of hours Ranjit traveled on foot and on horseback. The correct combination is 8 hours on foot and 2 hours on horseback.

Step-by-step explanation:

To solve this problem using the guess and check method, we need to find the number of hours Ranjit traveled on foot and on horseback. Let's start by assuming she traveled on foot for 10 hours. At a rate of 3 miles per hour, she would have traveled 3 x 10 = 30 miles. Since we know she traveled a total of 46 miles, she must have traveled on horseback for the remaining distance, which is 46 - 30 = 16 miles.

Now, let's assume she traveled on horseback for all 10 hours. At a rate of 7 miles per hour, she would have traveled 7 x 10 = 70 miles. This exceeds the total distance of 46 miles, so we know it is not possible for her to have traveled on horseback for the entire time.

By using these assumptions and testing different combinations of hours on foot and horseback, we find that the answer is 8 hours on foot and 2 hours on horseback. This allows for a total distance of 8 x 3 + 2 x 7 = 46 miles.

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