Let Rico's speed be X mph

THEN, Pedro's speed = 3X mph

Time taken by Rico = 45/X hours

Time taken by Pedro = 45 /3X = 15/X hours

Given 45/X - 15/X = 2 hours

30/X = 2

X = 15 mph = Rico's speed ANSWER

CHECK

45/15 = 3 hours

45/45 = 1 hour

3-1=2 hours

Distance = d miles

Let Rico speed be x mph

Rico time = d / x hours

Pedro speed = 3x mph

Pedro time = d / [3x ] hours

d / x = d / [ 3x ] + 2

45 / x = 45 / [ 3x ] + 2

135 + 45 + 6x

90 = 6x

x = 15

Rico speed = 15 mph

Pedro can drive 3 times as fast as Rico can ride his bicycle.

If it takes Rico 2 hours longer than Pedro to travel 45 miles,

how fast can Rico ride his bicycle

Let's begin by writing algebraic expressions to represent the two rates:

x = Rico's rate (mph)

3x = Pablo's rate (mph)

Next, let's write an equation to express the relationship between the two times

using the given distance and our algebraic expressions for the two rates:

distance = rate x time

time = distance / rate

Pedro's time: 45/3x

Rico's time: 45/x

45/3x + 2 = 45/x (two hours longer for Rico)

Next, let's solve our equation for x (Rico's rate):

45/3x + 2 = 45/x

(3x)(45/3x) + (3x)(2) = (3x)(45/x)

45 + 6x = 135

6x = 90

x = 15 mph (Rico's rate)

We can verify our answer by plugging it back into our equation

and checking to see that both sides are equal:

84/3x + 2 = 84/x

84/[(3)(28)] + 2 = 84/28

84/84 + 2 = 3

1 + 2 = 3

3 = 3 (both sides are equal)

Since both sides of the equation have been proven equal with our answer plugged in,

we are confident that our answer is correct.

Let r represent Rico's speed on the bicycle.

.. 45/r = 2 +45/(3r) . . . . time = distance / speed

.. 45/r -15/r = 2 . . . . . . subtract 45/(3r)

.. 30/r = 2 . . . . . . . . . . collect terms

.. 30/2 = r = 15 . . . . . . . multiply by r/2

Rico rides his bicycle at 15 miles per hour.