A man starts on a 290 mile trip at 10 a.m. and drives at an average speed of 40 mph until he stops for lunch. After he stops one-half hour for lunch, he finds that he must drive the rest of the way at an average speed of 50mph if he is to arrive by 5pm. When did he stop for lunch?
Let the distance from the restaurant to his final destination =D
The distance from his house to the restaurant =290 - D
[290 - D] / 40 =1/2 + D/50, solve for D
D = 150 miles
290 - 150 = 140 miles - distance from his house to the restaurant.
140 / 40 =3.5 hours - it took him to drive to the restaurant.
10:00 am + 3.5 =1:30 pm - when he stopped for lunch till he finished at 2:00 pm.
150 /50 =3 hours that he drove from 2:00pm till 5:00 pm, when he reached his final destination.