Question

Thomas bikes at a rate of 24 mi in 3 h. Thomas’s friend De’Monte bikes 9.5 mi each hour. De’Monte and Thomas are 105 mi apart and are biking towards each other. How long will the boys bike before they meet? How many miles will each boy have biked when they meet? Explain how to solve this problem one way—e.g., using a table, a diagram, a graph, equations, or words.

Answer 1

The boys will bikes= 6 hours before they meet.

Thomas has biked  48 miles when they meet.

and De'Monte has biked 57 miles when they meet.

Step-by-step explanation:

Given, Thomas bikes at a rate of 24 miles in 3 hours. Thomas's friend De'Monte bikes 9.5 miles each hour. De'Monte and Thomas are 105 miles apart and are biking towards each other.

Thomas bikes $(\frac{24}{3} ) miles$ = 8 miles each hour.

The relative velocity of Thomas and De'Monte is =(8+9.5) miles = 17.5 miles per hour.

The boys will bikes =$\frac{distance}{speed}$ =$\frac{105}{17.5}$ hours = 6 hours before they meet.

Thomas has biked = (8×6) miles = 48 miles when they meet.

and De'Monte has biked = (9.5 × 6) miles = 57 miles when they meet.