Speed Problem - Speed Problem

SOURCE:COMPETITION
Number of Problems: 10. : (Book)

Mr. Earl E. Bird gets up every day at 8:00 AM to go to work. If he drives at an average speed of 40 miles per hour, he will be late by 3 minutes. If he drives at an average speed of 60 miles per hour, he will be early by 3 minutes. How many miles per hour does Mr. Bird need to drive to get to work exactly on time?

$ext{(A)} 45 qquad ext{(B)} 48 qquad ext{(C)} 50 qquad ext{(D)} 55 qquad ext{(E)} 58$

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

$mathrm{(A) } 250 qquad mathrm{(B) } 300 qquad mathrm{(C) } 350 qquad mathrm{(D) } 400qquad mathrm{(E) } 5...$

Doug can paint a room in $5$ hours. Dave can paint the same room in $7$ hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let $t$ be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by $t$ ?

$mathrm{(A)} left(frac{1}{5}+frac{1}{7} ight)left(t+1 ight)=1qquadmathrm{(B)} left(frac{1}{5}+frac{1}{7} ight)t...$

Shelby drives her scooter at a speed of $30$ miles per hour if it is not raining, and $20$ miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the evening, for a total of $16$ miles in $40$ minutes. How many minutes did she drive in the rain?

$extbf{(A)} 18 qquad extbf{(B)} 21 qquad extbf{(C)} 24 qquad extbf{(D)} 27 qquad extbf{(E)} 30$

Eric plans to compete in a triathlon. He can average $2$ miles per hour in the $frac{1}{4}$ -mile swim and $6$ miles per hour in the $3$ -mile run. His goal is to finish the triathlon in $2$ hours. To accomplish his goal what must his average speed in miles per hour, be for the $15$ -mile bicycle ride?

$mathrm{(A)} frac{120}{11}qquadmathrm{(B)} 11qquadmathrm{(C)} frac{56}{5}qquadmathrm{(D)} frac{45}{4}qquadmath...$

Andrea and Lauren are $20$ kilometers apart. They bike toward one another with Andrea traveling three times as fast as Lauren, and the distance between them decreasing at a rate of $1$ kilometer per minute. After $5$ minutes, Andrea stops biking because of a flat tire and waits for Lauren. After how many minutes from the time they started to bike does Lauren reach Andrea?

$mathrm{(A)} 20qquadmathrm{(B)} 30qquadmathrm{(C)} 55qquadmathrm{(D)} 65qquadmathrm{(E)} 80$

Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds. Working together, how many cupcakes can they frost in 5 minutes?

$extbf{(A)} 10qquad extbf{(B)} 15qquad extbf{(C)} 20qquad extbf{(D)} 25qquad extbf{(E)} 30$

10.