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# Math problems about miles and hours

PS: THERE ARE 2 QUESTIONS. PLZ ANSWER BOTH OF THEM!

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?

10)A private jet had been flying for 2 hours when it encountered strong head wings which reduced its speed by 40 miles per hour. If it took the plane 5 hours to travel 1,280 miles, find its peed before flying into the head winds.

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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 = 5-2 = 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 = 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)