Question

Ten minutes after he left his home, Gerald was 40 miles from his grandmother’s house. Then, 22 minutes after he left, he was 34 miles from her house. If he was traveling toward his grandmother’s home at a constant rate and reached her house after 90 minutes, how far away from her house does he live?
A step-by-step would be most appreciated, thank you! (15 pts)

Answer 1

After 10 minutes, he's 40 miles away. After 22 minute, he's 34 miles away. Therefore, in those 12 minutes between, he covered 6 miles. We can make a ratio out of this: 6/12 = 0.5, so he is walking at a rate of 0.5 mi/min (miles per minute). Finally, we can set x/90 equal to 0.5/1 because he is walking at the same rate the entire time. Cross multiply to solve for x. Finally, you get that he had to travel 45 miles in 90 minutes, so his home is 45 miles away from his grandmother's.