Question

Question

Answer 1

Missing from the question

Aletheia's speed is 0.6 miles per hour slower than Elvira's speed.

Answer:

$s_E = 3.0$

$s_A = 2.4$

Step-by-step explanation:

Given

$d = 3.2m$ -- distance

$t_E = 1/2$ --- Elvira time

$t_A = 2/3$ --- Aletheia time

$s_E - s_A = 0.6$ --- the relationship between their speeds

Required

Their walking speed

Distance (d) is calculated as:

$d = speed * time$

For Elvira, we have:

$d_E = s_E * 1/2$

For Aletheia, we have:

$d_A = s_A * 2/3$

So, we have:

$d_E + d_A = d$ --- total distance

This gives:

$s_E * 1/2 + s_A * 2/3 = 3.2$

Recall that:

$s_E - s_A = 0.6$

Make sE the subject

$s_E = 0.6+s_A$

Substitute $s_E = 0.6+s_A$ in $s_E * 1/2 + s_A * 2/3 = 3.2$

$(0.6+s_A)* 1/2 + s_A * 2/3 = 3.2$

$0.3+1/2s_A + 2/3s_A = 3.2$

Collect like terms

$1/2s_A + 2/3s_A = 3.2-0.3$

$1/2s_A + 2/3s_A = 2.9$

Express all as decimal

$0.5s_A + 0.7s_A= 2.9$

$1.2s_A= 2.9$

Divide both sides by 1.2

$s_A = 2.4$

Recall that:

$s_E = 0.6+s_A$

So, we have:

$s_E = 0.6+2.4$

$s_E = 3.0$