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

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

A. Ryan left the science museum and drove south. Gabriella left three hours later driving 42 km/h faster in an effort to catch up to him. After two hours Gabriella finally caught up. Find Ryan\'s average speed.

B. A submarine left Hawaii two hours before an aircraft carrier. The vessels traveled in opposite directions. The aircraft carrier traveled at 25 mph for nine hours. After this time the vessels were 280 mi. apart. Find the submarine\'s speed.

C. Kali left school and traveled toward her friend\'s house at an average speed of 40 km/h. Matt left one hour later and traveled in the opposite direction with an average speed of 50 km/h. Find the number of hours Matt needs to travel before they are 400 km apart.

Please show all work and give full explanations. No handwritten work please.

Solution

A. Let Ryan\'s average speed be x kph. Then Gabriella\'s average speed is x + 42 kph. Since Gabriella left 3 hours after Ryan and drove for 2 hours before catching up with Ryan, therefore, Ryan has been driving for 3 + 2 = 5 hours when they caught up. In 5 hours, Ryan travelled 5x km. In 2 hours, Gabriella travelled 2(x +42)km. Then, we have 5x = 2(x + 42) or, 5x = 2x + 84 or 5x - 2x = 84, or, 3x = 84 so that x = 84/3 = 28. Thus Ryan\'s average speed is 28 kph.

B. The submarine left 2 hours before the aircraft carrier .When the aircraft carrier has travelled for 9 hours, the submarine has travelled for 9 + 2 = 11 hours. Let the submarine\'s speed be xmph. In 11 hours, the submarine will travel 11x miles. In 9 hours, the aircraft carrier travelling @ 25 mph will travel 9* 25 = 225miles. Since the submarine and the aircraft carrier are travelling in opposaite directions, the total distance between these two vessels is the sum of the distances travelled . Thus, we have 11x + 225 = 280 or, 11x = 280 - 225 = 55 so that x = 55/11 = 5. Thus, the submarine\'s speed is 5 mph.

C. Let Matt be travelling for x hours before he and Kali are 400 km apart. Since Kali left 1 hour before Matt, she has travelled for x + 1 hour before she and Matt are 400 km apart. In x + 1 hour, travelling @ 40kph, the distance travelled by Kali is 40(x +1). The distance travelled by Matt in x hours @ 50 kph is 50x. Since Kali and Matt are travelling in opposaite directions, the total distance between them is the sum of the distances travelled i.e. 40(x + 1) + 50x. Since Kali and Matt are 400 km apart, we have 40(x + 1) + 50x. = 400 or, 40x + 40 + 50x = 400 or, 90x = 400 - 40 or, 90x = 360 so that x = 360/90 = 4. Thus matt needs to travel for 4 hours before he and Kali are 400km apart.