Question

Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle? Round your answer to two decimal places, if needed.

Answer 1

`\huge \boxed{ \boxed{ \red{ \tt17 \: mph}}}`

Explanation:

to understand this

you need to know about:

• equation
• equation word problems
• PEMDAS

given:

• Miguel can drive 4 times as fast as Raul can ride his bicycle. If it takes Raul 3 hours longer than Miguel to travel 68 miles, how fast (in mph) can Raul ride his bicycle

tips and formulas:

• t=d/s

to find

• how fast can Raul ride his bicycle

let's solve:

let's the speed of Raul be x

likewise

Miguel can drive 4 times as fast as Raul can ride his bicycle

therefore

4x

according to the question

`\sf (68)/(4x)+3=(68)/(x)`

`\implies \sf (68 + 12x)/(4x) = (68)/(x)`

`\sf factor \: out \: 4 \: and \: reduce \: it : \\ \sf \implies (4(17 + 3x))/(4x) = (68)/(x) \\ \\ \implies\sf (17 + 3x)/(x) = (68)/(x)`

`\sf multipy \: both \: sides \: by \: x : \\ \sf \implies ((17 +3 x)/(x) )x = ((68)/(x) )x \\ \implies \sf 17 + 3x = 68`

`\sf cancel \: 17 \: from \: both \: sides : \\ \implies \sf 17 - 17 + 3x = 68 - 17 \\ \implies \sf 3x = 51`

`\sf divide \: both \: side s \: by \: 3 : \\ \sf \implies (3x)/(3) = (51)/(3) \\ \therefore x = 17`

Answer 2

• 17 mph

Explanation:

• Miguel's speed = m, Raul's speed = r

Given

• m = 4r
• Distance = 68 miles
• Time difference = 3 hours

Solution

• time = distance/speed

Substitute values and solve for r the equation of the time difference:

• 68/m + 3 = 68/r
• 68/4r + 3 = 68/r
• 17/r + 3 = 68/r
• 17 + 3r = 68
• 3r = 68 - 17
• 3r = 51
• r = 17

Raul's speed is 17 mph