Check Your Skills Answer Key

  1. 36,000 meters/hour

    First convert seconds to minutes. There are 60 seconds in a minute, so 10 m/sec × 60 sec/min = 600 m/min.

    Now convert minutes to hours. There are 60 minutes in 1 hour, so 600 m/min × 60 min/hr = 36,000 m/hr.

  2. 30 hours

    First simplify the rate: , which is the same as 15 gal/min. The question asks for the number of hours it will take to fill the pool, so convert minutes to hours. There are 60 minutes in an hour, so the rate is 15 gal/min × 60 = 900 gal/hr. Now you can set up an RTW chart. Let t be the time it takes to fill the pool:

      R
    (gal/hr)    		 × T
    (hr)    		 = W
    (gallons)
    inlet pipe 900 ×  t = 27,000

    Now solve for t:

  1. (E)

    Organize this information in an RTD chart as follows:

      R
    (mi/hr)    		 × T
    (hr)    		 = D
    (mi)
    Adrienne 3 ×
    		 t + 1 =
    		 d
    James 4 ×
    		 t =
    		 d
    Total —
    		—
    		2d

    Set up algebraic equations to relate the information in the chart, using the RT =­ D ­equation.

    Adrienne: 3(t + 1) = d
    James: 4t = d

    Notice that the d here is not 60 miles, since neither Adrienne nor James have walked all the way from X to Y. Rather, d represents how far each person has walked when James catches up to Adrienne. At that point in time, they will have both walked the same distance from Town X toward Town Y.

    Substitute 4t for d in the first equation:

    Therefore, d = 4(3), which equals 12 miles.

  2. (D)

    Fill in the RTD chart. Nicky starts 12 seconds before Cristina, so Nicky’s time is t + 12.

      R
    (m/s)    		 × T
    (second)    		 = D
    (meter)
    Cristina 5 ×
    		 t =
    		 5t
    Nicky 3 ×
    		 t + 12 =
    		 3(t + 12)

    Write expressions for the total distance, and then set these two distances equal to each other.

    Therefore, Nicky will have run for 18 + 12 = 30 seconds before Cristina catches up to him.

  1. 4.5 mph

    Assume a Smart Number for the distance to school. The Smart Number should be divisible by 9 and 3. The simplest choice is 18 miles for this distance. Now solve:

    • Time biking: T = D/R = 9/9 = 1 hr
    • Time walking: T = D/R = 9/3 = 3 hr
    • Total time: 1 hr + 3 hr = 4 hr
  1. 2.5 hours

    If Sophie addresses 20 envelopes in 1 hour, then the rate at which she addresses is 20 envelopes/hr. Set up an RTW equation:

    20 envelopes/hr × T = 50 envelopes

    T = 50/20 = 2.5 hr

  2. 3,750 feet

    The rate at which the steel mill produces I-beams is Next, set up an RTW equation. Let w represent the number of feet of I-beam produced:

  3. 6 minutes

    Always express work rates as jobs per unit of time. Remember that the combined rates for Tarik and Andy are additive:

  1. 6,400
    Time Population
    6 days ago 200
    4 days ago
    (Careful! Count by two days.)    		 400
    2 days ago 800
    NOW 1,600
    2 days from now 3,200
    4 days from now 6,400