Question

When Ace Airlines changed to planes that flew 100 km/h faster than its old ones, the time of its 2800 km Dallas-Seattle flight was reduced by 30 minutes. Find the speed of the new planes.

Answer 1

we know speed = distance/time.
look at the old plane first:
v-100 = 2800/t since the old plane is 100km/h slower than the new one
now the new plane:
v=2800/(t-0.5) since the it takes half an hour less.
we now get two simultaneous equations
(v-100)t=2800 ...1
(t-0.5)v=2800 ...2

subtracting one from the other we get v=200t. substituting this into 1 we get
(200t-100)t=2800 a quadratic equation which simplifies to
2t^2-t-28=0 this gives t=-7/2 or t=4. since t>0, t=4 only makes physical sense

finally using t=4 in the equation for v, we get v=800km/h