Let c1 and c2 be the times
for connections after Limousine and plane journeys respectively. Let Limousine
take t1 hours to travel S1 miles. Let the plane take t2 hours to travel S2
miles. Then the car takes t3 = (5.5 - t1 - t2 - c1 - c2) hours to cover S3 = (750-
S1 - S2) miles. Let c1+c2 = c = total connection time
S1 =
55 t1 S2 = 400 t2 S3 = 40 t3
t1 + t2 + t3 + c = 5.5 hours,
Limousine takes as long as
the car & connections,
t1 =
t3 + c -- equation 3
So, t1 + t2 + t1 = 5.5
2 t1 = 5.5 – t2 --- equation 1
The plane travelled distance
4 times as far as limousine and car combined
S2 = 4 ( S1 + S3)
But S1+S2+S3 = 750 miles,
so
S1 + 4 (S1+S3) + S3 = 750 => S1+S3 = 150 miles --- equation 2
S2 = 600 miles
t2 = S2/400 mph = 1.5 hours
Substitute t2 in equation
1, we get
2 t1 = 5.5 – 1.5 = 4 =>
t1 = 2 hours
So
S1 = 2*55 = 110 miles
S3 = 150 – 110 = 40 miles -- using equation 2
t3 = S3/40 mph = 1 hour
From equation 3 , we have
t3 + c = 2 hours
So C = 2- t3 = 1 hours
