Question

Car A starts in Sacramento at 11am. It travels along 400 mile route to Los Angeles at 60 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet?

Answer 1

• 38.89 miles

Step-by-step explanation:

from the question we have the following:

distance between Sacramento and los angles = 400 miles

speed of car A = 60 mph

start time of car A = 11 am

speed of car B = 75 mph

start time of car B = 12 pm

distance of Fresno from Los Angeles = 150 miles

• To start off let's allow car A to travel for one hour (from 11 am to 12 pm), during which it would have covered a distance of 60 miles.
• Now the time would be 12 pm and the distance between the two cars would be 400 - 60 (distance traveled by car A within 11 am to 12 pm) = 340 miles
• From 12 pm to the time both cars will meet, the distance covered by car A + distance covered by car B would be equal to 340 miles. Therefore
• Distance covered by car A = speed x time(t) = 60 x t = 60t
• Distance covered by car B = speed x time(t) = 75 x t = 75t
• 60t + 75t = 340 miles
• 135t = 340
• t = 2.51 hours
• Recall that at their meeting point, the distance covered by car B = 75t = 75 x 2.62 = 188.89 miles
• Since Fresno is 150 miles from Los Angeles, car B which is 188.89 miles from Los Angeles at their meeting point would be 188.89 - 150 = 38.89 miles from Fresno
• 38.89 miles would also be the distance of car A from Fresno since that is their meeting point.