1 Solve the 3 parts of the following Distance Rate Time ques

1. Solve the 3 parts of the following Distance- Rate- Time question:

A. Chelsea left the White House and traveled toward the capital at an average speed of 34 km/h. Jasmine left at the same time and traveled in the opposite direction with an average speed of 65 km/h. Find the number of hours Jasmine needs to travel before they are 59.4 km apart.

B. Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose\'s average speed.

C. Jose left the White House and drove toward the recycling plant at an average speed of 40 km/h. Rob left some time later driving in the same direction at an average speed of 48 km/h. After driving for five hours Rob caught up with Jose. How long did Jose drive before Rob caught up?

Please solve each and give a thorough explanation as to how you arrive at the answer. Please no handwritten work.

Solution

A. Let x be the number of hours that Jasmine travels before she and Chelsea are 59.4 km apart. Chelsea will travel 34x km in x hours while Jasmine will travel 65x km in x hours. Since Chelsea and Jasmine are travelling in opposaite directions, therefore, the sum of the distances travelled by them together is the distance between them. Then, we have 34x + 65x = 59.4, or, 99x = 59.4 so that x = 59.4/99 = 0.6 hour or 0.6*60 = 36 minutes. The answer is 0.6 hour.

B.Let Jose\'s average speed be x mph. Then Kyla\'s average speed is x + 35 mph.Since Kyla left 2.1 hours after Jose and caught up with Jose, Jose had travelled hor 2.1+ 1.2 = 3.3 hours and Kyla had travelled for 1.2 hours when they caught up. In 3.3 hours, the distance travelled by Jose is 3.3x. In 1.2 hours, the distance travelled by Kyla is 1.2(x + 35). Therefore, we have 3.3x = 1.2 ( x+ 35) or, x + 35 = (3.3/1.2 )x = 2.75 x > Thus 2.75x - x = 35 or, 1.75x = 35 so that x = 35/1.75 = 20. Thus, Jose\'s average speed is 20kph.

C.Let the time difference between the start of journey by Jose and Rob be x hours. If Rob has been driving for 5 hours, then Jose has been driving for x + 5 hours. The distance travelled by Jose in x + 5 hours is 40(x + 5). Also, the distance travelled by Rob in 5 hours is 48*5 = 240km. Thereore, we have 40(x + 5) = 240, or, x + 5 = 240/40 = 6. Therefore, x = 6 - 5 = 1. Thus Jose drove for x + 5 = 6 hours before caught up.