<p>At \(0800\text{ hrs}\), Bernard cycles from Town \(A\) to Town \(B\) which is \(100\text{ km}\) apart. Town \(M\) is half-way between Town \(A\) and Town \(B\). Bernard's average speed from Town \(A\) to Town \(M\) is \(x\text{ km/h}\). From Town \(M\) to Town \(B\), his average speed is increased by \(2\text{ km/h}\). The difference in time taken is \(20\) minutes.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Write down an expression for the time taken to travel</div><ol class="i-list"><li data-list-item-id="item-a-i" data-list-item-path="item-a/item-a-i"><div class="list-item-paragraph">from Town \(A\) to Town \(M\),<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-a-ii" data-list-item-path="item-a/item-a-ii"><div class="list-item-paragraph">from Town \(M\) to Town \(B\).<span class="inline-marks">[1]</span></div></li></ol></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Using your answers in <strong>(a)</strong>, form an equation and show that it can be simplified to \(x^2 + 2x - 300 = 0\).<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Solve the equation \(x^2 + 2x - 300 = 0\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Find the time that Bernard arrives at Town \(B\).<span class="inline-marks">[2]</span></div></li></ol>

At \(0800\text{ hrs}\), Bernard cycles from Town \(A\) to Town \(B\) which is \(100\text{ km}\) apart. Town \(M\) is half-way between Town \(A\) and Town \(B\). Bernard's average speed from Town \(A\) to Town \(M\) is \(x\text{ km/h}\). From Town \(M\) to Town \(B\), his average speed is increased by \(2\text{ km/h}\). The difference in time taken is \(20\) minutes.

Write down an expression for the time taken to travel

Using your answers in **(a)**, form an equation and show that it can be simplified to \(x^2 + 2x - 300 = 0\).

Solve the equation \(x^2 + 2x - 300 = 0\).

Find the time that Bernard arrives at Town \(B\).

Quadratic Equations and Inequalities

Quadratic Equations and Inequalities