Slower plane will take 15 hours time to complete the flight of 1500miles distance .
What is speed?
" Speed is defined as the total distance travelled per unit time."
Formula used
Speed = (total Distance travelled) / (time taken )
According to the question,
Distance travelled = 1500 miles
'x' represents the speed of the slower plane
'h' represents the time taken to complete the trip by slower plane
Therefore,
'x + 25' represents the speed of the faster plane
'h-3' represents the time taken to complete the trip by faster plane
Substitute the value in the formula for slower and faster plane we get,
Faster plane : [tex]x +25 = \frac{1500}{h-3}[/tex] ____(1)
Slower plane : [tex]x= \frac{1500}{h}[/tex] _____(2)
Substitute the value of 'x' from (2) in (1) we get,
[tex]\frac{1500}{h} +25 = \frac{1500}{h-3}[/tex]
⇒[tex]25 = \frac{1500}{h-3}-\frac{1500}{h}[/tex]
⇒[tex]25 =1500( \frac{1}{h-3}-\frac{1}{h})[/tex]
⇒[tex]1 =60( \frac{h-h+3}{(h)(h-3)} )[/tex]
⇒[tex]1=(60)\frac{3}{h^{2} -3h}[/tex]
⇒[tex]h^{2} -3h -180=0[/tex]
⇒[tex]h^{2} -15h+12h -180=0[/tex]
⇒[tex](h-15)(h+12)=0[/tex]
⇒ [tex]h=15 or h=-12[/tex]
Time cannot be negative.
Hence, time taken by slower plane to complete the trip is equals to
h = 15hours.
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