SOLUTION: Can you please help me find the formula for this question? A jet left Singapore five hours before a passenger plane. The planes flew in opposite directions. The passenger plane fl

Question 1147215: Can you please help me find the formula for this question?
A jet left Singapore five hours before a passenger plane. The planes flew in opposite directions. The passenger plane flew 315 mph for four hours. After this time the planes were 5670 miles apart. What was the jet's speed?
Found 3 solutions by Theo, josmiceli, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rate * time = distance.

the passenger plan flew 315 miles per hour for 4 hours.
that means it traveled 315 * 4 = 1260 miles.

the jet flew 5 more hours for a total of 9 hours and flew 5670 - 1260 = 4410 miles.

the jets's speed was 4410 / 9 = 490 miles per hour.

your formulas would be:

r * t = d
let r1 and t1 and d1 be the formula for the passenger plane.
let r2 and t2 and d2 be the formula for the jet.

since they were going in opposite directions, their distance traveled was additive.

you get d1 + d2 = 5670.
since r1 * t1 = d1 and r2 * t2 = d2, then you get:
r1 * t1 + r2 * t2 = 5670

since the passenger plane flew 315 miles per hour in 4 hours, then r1 = 315 and t1 = 4 and the formula for the passsenger plane becomes 315 * 4 = d1
solve for d1 to get d1 = 4 * 315 = 1260 and the formula for the passenber plane becomes 315 * 4 = 1260

since the jet left 5 hours before the passenger plane, then t2 = t1 + 5
since t1 = 4, then t2 = 4 + 5 = 9.

since d1 + d2 = 5670, and since d2 = 1260, then d1 = 5670 - 1260 = 4410.

you get t1 = 9 and d1 = 4410 and the formula becomes r1 * 9 = 4410.
solve for r1 to get r1 = 4410 / 9 = 490.

the formula for the jet becomes 490 * 9 = 4410
the formula for the passenger plane becomes 315 * 4 = 1260
d1 + d2 = 5670
r1 * t1 + r2 * t2 becomes 490 * 9 + 315 * 4 = 5670.

either way you slice it, the answer is the same.
the jet's speed is 490 miles per hour.

the formula that helped to answer this question is rate * time = distance.
the rest was mostly logic.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the jet's speed in mi/hr
The jet flew for miles until the passenger plane took off
( This is the jet's head start )
Let = the distance in miles the passenger plane flew
= the distance in miles the jet flew
----------------------------------------------------------------------
Equation for the passenger plane
(1)
Equation for the jet
(2)
---------------------------------------
(1)
Plug (1) into (2)
(2)
(2)
(2)
-------------------------
The jet's speed is 490 mi/hr
----------------------------------
check:
(1)
(2)
(2)
(2)
(2)
OK
check the math & get another opinion if needed

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Can you please help me find the formula for this question?
A jet left Singapore five hours before a passenger plane. The planes flew in opposite directions. The passenger plane flew 315 mph for four hours. After this time the planes were 5670 miles apart. What was the jet's speed?

Let the jet's speed be S
The plane flew for 4 hours at 315 mph, or a distance of 4(315) = 1,260 miles
When the plane had flown 1,260 miles, the jet had flown 9 (5 + 4) hours, and 9S miles
When the jet had traveled 9S miles, and the plane 1,260 miles, the sum of their distances was 5,670 miles
We then get: 1,260 + 9S = 5,670
9S = 5,670 - 1,260
9S = 4,410
S, or jet’s speed was:
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