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Devon set out to bicycle from Exeter to the beach, a distance for 10 miles. After going a short while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The walk back to Exeter was made at a deected 3 miles per hour. The whole epsiode took 48 minutes. How many miles from Exeter did the flat occur?

Respuesta :

Answer:

Distance between Exeter and the point where flat tire occurred was 1.875 miles.

Step-by-step explanation:

Let the distance of Exeter and the point where bike developed the flat tire was = x miles

Then time taken to reach that point with speed 15 mi per hour = [tex]\frac{\text{Distance traveled}}{\text{Time taken}}[/tex]

= [tex]\frac{x}{15}[/tex] hours

Devon comes back with a speed of 3 miles per hour then time taken to come back = [tex]\frac{x}{3}[/tex] hours

Total time for the entire episode = 48 minutes or [tex]\frac{3}{4}[/tex] hours

Therefore, [tex]\frac{x}{15}+\frac{x}{3}=\frac{3}{4}[/tex]

[tex]\frac{x+5x}{15}=\frac{3}{4}[/tex]

[tex]\frac{6x}{15}=\frac{3}{4}[/tex]

x = [tex]\frac{3}{4}\times \frac{15}{6}[/tex]

x = [tex]\frac{15}{8}[/tex] miles

x = 1.875 miles

Therefore, distance between Exeter and the point where flat tire occurred was 1.875 miles.