Question

2727. Boat Y and boat Z start traveling toward each other from 600 mile apart. Y istraveling at 35 mph, Z at 40 mph. How many hours will pass before theymeet?a. 7 b. 8 c. 9 d. 102828. Refer to problem 27. Y and Z start traveling toward each other from 600miles apart. Y is traveling at 35 mph, Z at 40 mph. How many miles will Ytravel before they meet?a. 400 b. 320 c. 350 d. 280

Answer 1

27.It is given that boat Y and Z are travelling towards each other, the speed of both boats are given.

Y is 35mph and Z is 40mph.

Both boats are 600 miles apart. This can be understood by schematic below:

At the meeting point, the time will be same.

It is known that:

$\begin{gathered} \text{ Speed= Distance/time} \\ \text{time}=\text{ Distance/Speed} \end{gathered}$

Let the Distance travelled by Boat Y be Dy and distance travelled by boat Z be Dz, so it follows:

$\begin{gathered} \frac{D_y}{35}=\frac{D_z}{40} \\ \frac{D_y}{D_z}=\frac{35}{40}=\frac{7}{8} \end{gathered}$

Since Dy+Dz=600, so it follows:

$\begin{gathered} D_z+\frac{7}{8}D_z=600 \\ \frac{15}{8}D_z=600 \\ D_z=320\text{ miles} \end{gathered}$

So the time is given by:

$t_z=t_y=\frac{D_z}{40}=\frac{320}{40}=8\text{ hours.}$

So they meet in 8 hours. Option B is correct.

28. As already calculated that Z will travel 320 miles, so Y will travel 280 miles.

Option D is correct.