9) A jet bomber traveling 500 miles per hour arrived over its target at the same time as its fighter jet escort which left the same base 1/2 hour after the bomber took off. How many hours did it take to reach the target if the fighter jet traveled 600 miles per hour?
jet bomber speed = 500 mph
Fighter jet speed = 600 mph
Distance is same for both = x miles
Since speed = distance per unit time then time = distance/speed
jet bomber time = x/500
fighter jet time = x/600
jet bomber time = fighter jet time + 1/2
Substitute and solve for x.
x/500 = x/600 + 1/2
6x = 5x + 1500 (multiply each term by LCD 5*600=3000 to remove fractions)
6x  5x = 1500 isolate variable
x = 1500 miles
Final answer: jet bomber time = 1500 mi/500 mph = 3 hrs for jet bomber to reach target
10)A private jet had been flying for 2 hours when it encountered strong head winds which reduced its speed by 40 miles per hour. If it took the plane 5 hours to travel 1,280 miles, find its speed before flying into the head winds.
before head winds speed = x
head winds speed = x  40 mph
Use speed = distance/time for each part
Total time = 5 hrs
before head winds time = 2 hrs
head winds time = 52 = 3 hrs
Find out distance traveled with head wind:
distance = speed*time
head winds speed = x  40 mph
head winds distance = (x  40 mph) * 3 hrs = 3x  40*3 = 3x  120 mi
Find out distance traveled before head wind:
Total distance = 1280 mi.
Before head winds distance = before head winds speed * before head winds time
Before head winds distance = x*2 = 2x mi.
Add distances to equal total distance:
(3x  120) + 2x = 1280 mi
5x  120 = 1280 add like terms
5x = 1280 + 120 isolate term with variable
5x = 1400
x = 1400/5 = 280 mph (before head winds speed)
Check answer:
before head winds distance =
2hr*280 mph = 560 mi.
head winds speed = 280 mph  40 mph = 240 mph
head winds distance = 3 hrs * 240 mph = 720 mi.
Total distance= 560 mi. + 720 mi. = 1280 mi.
Final answer: speed before flying into head winds is 280 mph
7/12/2016

Chris B.