Problem 1) Distance equals 120 miles
Equation: 150-D=30(3-T)
150-60T=90-30T
T=2
D=R.T
D=60.2=120miles

Problem2) Obviously the car is faster than the bus. Check your numbers in the problem. I dont think they are correct

Problem 1


let's assume the following:

r1 = speed from Home to Airport = 30 mph
r2 = speed from Airpot to Office = 60 mph

d = total distance = 150 miles = d1 (Home - Airport) + d2 (Airport - Office), hence d1 = d -d2
t = total time = 3 hours = t1 +t2

we know fron basic physics that r1 = d1 / t1 and r2 = d2 / t2, hence t1 = d1 / r1 and t2 = d2 / r2

The purpose of the problem is to find d2


starting with t = t1 + t2, we can build the following (step by step):
t = d1/r1 + d2/r2
t = (d-d2)/r1 + d2/r2
t = d/r1 - d2/r1 +d2/r2
t = d/r1 + d2(1/r2-1/r1)
t = d/r1 + d2(r1-r2)/r1r2

then

d2 = (t-d/r1) x r1r2 / (r1-r2)

d2 = 120 miles


Problem 2


let's assume the following:

rC = speed of the car
rB = speed of the bus

dB = distance covered by the car during the 2-hour trip
dC = distance covered by the bus during that 2-hour trip

t = 2 hours

and basic physics which thought us once that r = d / t

we know from the context that:
rC = 2rB - 30
dC = dB + 20, i.e. dB = dC - 20

Purpose of the problem is to find rC


starting with rC = 2rB - 30, we can build the following:

rC = 2dB/t - 30
rC = 2(dC - 20)/t - 30
rC = 2dC/t - 40/t - 30
rC = 2rCt/t - 40/t - 30
rC = 2rC - 40/t - 30

then
rC = 40/t + 30
rC = 20 + 30
rC = 50 mph