Respuesta :
Answer:
2.5
Step-by-step explanation:
56(t+1/2)=70 t
56T + 28= 70T
28=70T-56T
28=14
2=T
s=T+ 1/2
S=2+ 1/2
S=2.5 hours
"Stephanie left riverside, California, driving her motorhome north on interstate 15 towards Salt Lake City at a speed of 56 miles per hour. Half an hour later , tina left riverside in her car on the same route as Stephanie , driving 70 miles per hour. Solve the system.
{56s=70t
{s=t+1/2
for t to find the value of s, the number of hours Stephanie will have driven before Tina catches up to her. "
Answer:
On solving the system, we get t = 2 and s = 2.5
The number of hours Stephanie will have driven before Tina catches up to her is 2.5 hours
Solution:
According to question,
Stephanie is driving at speed of 56 miles per hour
Half an hour later, tina started driving 70 miles per hour
The relation between speed and distance is:
[tex]Distance = speed \times time[/tex]
So, the extra distance travelled by Stephanie is:
[tex]\text { Distance }=56 \times \frac{1}{2}=28 \text { mile }[/tex]
According to question, the time that both Stephanie and Tina travel is the same, so we only need one variable for time "t "
Distance Travelled by Stephanie (d) + 28miles = Distance Travelled by Tina (D)
d + 28 = D
We already know that [tex]Distance = speed \times time[/tex]
[tex](56 \times t)+28=(70 \times t)[/tex]
56t + 28 = 70t
70t – 56t = 28
14t = 28
t = 2
Given that "s" represents the number of hours Stephanie will have driven before Tina catches up to her.
Now, its given that [tex]s = t + \frac{1}{2}[/tex]
So, [tex]s = 2 + \frac{1}{2}\\\\s = \frac{5}{2}\\\\s = 2.5[/tex]
So the number of hours Stephanie will have driven before Tina catches up to her is 2.5 hours
