Question

John decided to go for a hike. He hiked 4 miles up a mountain trail. His descent was 10% faster than his climb up the mountain Let r be his speed climbing up the mountain. What is an expression that represents his total time in hours hiking?

Answer 1

The expression that represents John's total time hiking is 4/r + 4/((1.10)r) hours.

Step-by-step explanation:

To calculate John's total time hiking, we need to consider the time it took for his ascent and descent separately. Let's say his speed while climbing up the mountain is r miles per hour. The time taken for his ascent is given by the distance divided by his speed, which is 4/r hours. Since his descent is 10% faster, his speed while descending is (1.10)r miles per hour. The time taken for his descent is given by the distance divided by his speed, which is 4/((1.10)r) hours.

Therefore, the total time taken by John for his hike is the sum of the time taken for his ascent and descent, which is 4/r + 4/((1.10)r) hours. This expression represents John's total time hiking in hours.