# 1.10 Distance, Rate and Time

A passenger and a freight train start toward each other at the same time from two points 300 miles apart. If the rate of the passenger train exceeds the rate of the freight train by 15 miles per hour, and they meet after 4 hours, what must the rate of each be?

Two automobiles started at the same time from a point, but traveled in opposite directions. Their rates were 25 and 35 miles per hour respectively. After how many hours were they 180 miles apart?

Two men are traveling in opposite directions at the rate of 20 and 30 miles an
hour at the same time and from the same place. In how many hours will they
be 300 miles apart?

A car traveling at 48 mph overtakes a cyclist who, riding at 12 mph, has had
a 3 hour head start. How far from the starting point does the car overtake
the cyclist?

Running at an average rate of 8 m/s, a sprinter ran to the end of a track and
then jogged back to the starting point at an average rate of 3 m/s. The
sprinter took 55 s to run to the end of the track and jog back. Find the
length of the track.

A, who travels 4 miles an hour starts from a certain place 2 hours in advance
of B, who travels 5 miles an hour in the same direction. How many hours
must B travel to overtake A?

A family drove to a resort at an average speed of 30 mph and later returned
over the same road at an average speed of 50 mph. Find the distance to the
resort if the total driving time was 8 hours.

Two trains travel toward each other from points which are 195 miles apart.
They travel at rate of 25 and 40 miles an hour respectively. If they start at the
same time, how soon will they meet?

An executive drove from home at an average speed of 40 mph to an airport
where a helicopter was waiting. The executive boarded the helicopter and
flew to the corporate offices at and average speed of 60 mph. The entire
distance was 150 mi. The entire trip took 3 h. Find the distance from the
airport to the corporate offices.

A is 60 miles from B. An automobile at A starts for B at the rate of 20 miles
an hour at the same time that an automobile at B starts for A at the rate of
25 miles an hour. How long will it be before the automobiles meet?