In the formula $s=\frac{d}{t}$ where $s$ is speed, $d$ is distance, and $t$ is time, how would you solve for time $t$?
a. $t=d s$
b. $t=\frac{s}{d}$
c. $t=\frac{d}{s}$
d. $t=s d$
Answer (1)
Start with the formula s = t d .
Multiply both sides by t to get s t = d .
Divide both sides by s to isolate t .
The solution is t = s d , so the answer is s d .
Explanation
Understanding the Problem We are given the formula s = f r a c d t , where s represents speed, d represents distance, and t represents time. Our goal is to isolate t on one side of the equation to solve for time.
Multiplying by t To solve for t , we can start by multiplying both sides of the equation by t . This gives us:
s t im es t = f r a c d t t im es t
Simplifying, we get:
s t = d
Dividing by s Now, to isolate t , we divide both sides of the equation by s :
f r a c s t s = f r a c d s
Simplifying, we find:
t = f r a c d s
Final Answer Therefore, the formula for time t in terms of speed s and distance d is t = f r a c d s . Comparing this to the given options, we see that option c, t = f r a c d s , is the correct answer.
Examples
Understanding how to solve for time is crucial in many real-world scenarios. For instance, if you're planning a road trip and know the distance you'll travel and your average speed, you can calculate the estimated travel time. Let's say you plan to drive 300 miles (d = 300) at an average speed of 60 miles per hour (s = 60). Using the formula t = f r a c d s , you can calculate the time: t = f r a c 300 60 = 5 hours. This helps you estimate when you'll arrive at your destination, plan for breaks, and manage your travel schedule effectively.
